Can an Amalekite convert to Judaism?

(8) Amalek came and fought with Israel at Rephidim.(9) Moses said to Joshua, “Pick some troops for us, and go out and do battle with Amalek. Tomorrow I will station myself on the top of the hill, with the rod of God in my hand.”(10) Joshua did as Moses told him and fought with Amalek, while Moses, Aaron, and Hur went up to the top of the hill.(11) Then, whenever Moses held up his hand, Israel prevailed; but whenever he let down his hand, Amalek prevailed.(12) But Moses’ hands grew heavy; so they took a stone and put it under him and he sat on it, while Aaron and Hur, one on each side, supported his hands; thus his hands remained steady until the sun set.(13) And Joshua overwhelmed the people of Amalek with the sword.

(14) Then ה׳ said to Moses, “Inscribe this in a document as a reminder, and read it aloud to Joshua: I will utterly blot out the memory of Amalek from under heaven!”(15) And Moses built an altar and named it Adonai-nissi. (16) He said, “It means, ‘Hand upon the throne of ה׳ !'ה׳ will be at war with Amalek throughout the ages.”

(17) Remember what Amalek did to you on your journey, after you left Egypt—(18) how, undeterred by fear of God, he surprised you on the march, when you were famished and weary, and cut down all the stragglers in your rear.(19) Therefore, when your God ה׳ grants you safety from all your enemies around you, in the land that your God ה׳ is giving you as a hereditary portion, you shall blot out the memory of Amalek from under heaven. Do not forget!

(188) To exterminate the seed of Amalek...

(189) To constantly remember what Amalek did to us...

(59) Not to forget the wicked deeds which Amalek perpetrated against us...

Israel was commanded to fulfill three mitzvot upon entering the Promised Land: to choose a king...to wipe out the descendents of Amalek...and to build God's Chosen House...

A king should not wage other wars before a milchemet mitzvah. What is considered as milchemet mitzvah? The war against the seven nations who occupied Eretz Yisrael, the war against Amalek, and a war fought to assist Israel from an enemy which attacks them...

...it is a positive commandment to destroy the memory of Amalek...It is also a positive commandment to constantly remember their evil deeds and their ambush of Israel to arouse our hatred of them...it is forbidden to forget our hatred and enmity for them.

The Sages taught in a baraita: Naaman the Aramean (see II Kings, chapter 5) was a ger toshav, meaning that he accepted upon himself to refrain from idol worship but did not convert to Judaism. Nebuzaradan was a completely righteous convert. Among the descendants of Sisera (see Judges, chapter 4) were those who studied Torah in Jerusalem. Among the descendants of Sennacherib were those who taught Torah in public. The Gemara asks: And who are they? The Gemara answers: They were Shemaya and Avtalyon.The baraita continues: Among the descendants of Haman were those who studied Torah in Bnei Brak. And even among the descendants of that wicked person, Nebuchadnezzar, were those whom the Holy One, Blessed be He, sought to bring beneath the wings of the Divine Presence and have them convert. The ministering angels said before the Holy One, Blessed be He: "Master of the Universe: The one who destroyed Your House and burned Your Sanctuary, will You introduce him beneath the wings of the Divine Presence?"...

(1) After the death of Saul—David had already returned from defeating the Amalekites—David stayed two days in Ziklag.(2) On the third day, a man came from Saul’s camp, with his clothes rent and earth on his head; and as he approached David, he flung himself to the ground and bowed low.(3) David said to him, “Where are you coming from?” He answered, “I have just escaped from the camp of Israel.”(4) “What happened?” asked David. “Tell me!” And he told him how the troops had fled the battlefield, and that, moreover, many of the troops had fallen and died; also that Saul and his son Jonathan were dead.(5) “How do you know,” David asked the young man who brought him the news, “that Saul and his son Jonathan are dead?”(6) The young man who brought him the news answered, “I happened to be at Mount Gilboa, and I saw Saul leaning on his spear, and the chariots and horsemen closing in on him.(7) He looked around and saw me, and he called to me. When I responded, ‘At your service,’(8) he asked me, ‘Who are you?’ And I told him that I was an Amalekite.(9) Then he said to me, ‘Stand over me, and finish me off, for I am in agony and am barely alive.’-a(10) So I stood over him and finished him off, for I knew that he would never rise from where he was lying.-a Then I took the crown from his head and the armlet from his arm, and I have brought them here to my lord.”(11) David took hold of his clothes and rent them, and so did all the men with him.(12) They lamented and wept, and they fasted until evening for Saul and his son Jonathan, and for the soldiers of the LORD and the House of Israel who had fallen by the sword.

(13) David said to the young man who had brought him the news, “Where are you from?” He replied, “I am the son of a resident alien, an Amalekite.”(14) “How did you dare,” David said to him, “to lift your hand and kill the LORD’s anointed?”(15) Thereupon David called one of the attendants and said to him, “Come over and strike him!” He struck him down and he died.(16) And David said to him, “Your blood be on your own head! Your own mouth testified against you when you said, ‘I put the LORD’s anointed to death.’”

He said, “It means, ‘Hand upon the throne of ה׳! (Shemos 17:16)...

R' Yehoshua said, "When the Holy One, blessed be He sits on His kingly throne and dominion is his, at that moment 'ה׳ will be at war with Amalek' (ibid.)."

R' Eliezer said, "God swears by His Throne of Glory that not a single child or grandchild will be left of Amalek under the entire sky, so no one will say 'this camel used to belong to Amalek, this lamb used to belong to Amalek.'"

R' Eliezer said, "God swears by His throne that if a member of any nation comes to convert, Israel should accept them but if one comes from the house of Amalek (Israel) should not accept them, as the verse says, "David said to the young man who had brought him the news, 'Where are you from?' He replied, 'I am the son of a resident alien, an Amalekite.'" (II Shmuel 1:13). At that moment David remembered that Moses was told that if a member of any nation comes to convert, Israel should accept them but if one comes from the house of Amalek (Israel) should not accept them. "And (David) said to him, 'Your blood be on your own head because your own mouth testified against you!...'" (II Shmuel 1:16). That's why the verse says "throughout the ages" (Shemos 17:16)."

...neither a milchemet hareshut or a milchemet mitzvah, should not be waged against anyone until they are offered the opportunity of peace...If the enemy accepts the offer of peace and commits itself to the fulfillment of the seven mitzvot that were commanded to Noah's descendents, none of them should be killed. Rather, they should be subjugated...

It is forbidden to lie when making such a covenant or to be untruthful to them after they have made peace and accepted the seven mitzvot.

(17) Whenever any of the gentiles convert and accept all of the mitzvot in the Torah...they are considered as Jews with regard to all matters...A convert may marry within the Jewish community immediately, i.e., a male convert...may marry a native-born Jewess and an Israelite may marry a female convert...There are four nations from which [converts] are exceptions: Ammon, Moab, Egypt, and Edom. When a person from one of these nations converts, he is like an Israelite with regard to all matters with the exception of marriage within the Jewish community.

...Perhaps one can say that the nations (trace ancestry) through the male (line), and these were converts (who descended) from the daughter of Haman, while the(ir) male (father) was from a different nation...

...the more likely view, in my opinion, is that they were (fathered) by a gentile from Haman's house who raped a Jewish girl, in which case the child would be legitimate...and even according to those who hold that the child is illegitimate, one can say that if they accepted (Torah and mitzvos) and converted, and only after that did it become known that they descended from Amalek...but nevertheless would be considered legitimate and completely Jewish according to everyone...

(1)The Month of Adar / Can an Amalekite Save Himself or Convert to Judaism?

(2) Even though the Torah commands us to wipe out the descendants of Amalek, if an Amalekite agrees to observe the seven Noahide laws, he no longer has the status of an Amalekite, and one may not kill him...

(3) Moreover, even if the Amalekites do not volunteer to observe the seven Noahide laws, we are commanded to offer them peace before waging war against them. That is, we offer them the opportunity to adopt the seven Noahide laws and to agree to be subservient to, and pay tribute to, the Jewish people. If they accept these conditions of peace, we do not wage war against them. If they refuse, however, we fight them until they are eradicated...

(4) The poskim disagree about whether an Amalekite who wants to convert to Judaism may be accepted. Rambam maintains that an Amalekite may convert. Accordingly, the Sages state that descendants of Haman, who was himself of Amalekite stock, taught Torah in Bnei Brak. Thus, our forebears accepted converts from the descendants of Amalek.

(5) Others assert that we do not accept Amalekite converts. This is the view of R. Eliezer, cited in the Mekhilta (end of Parashat Beshalaḥ), who relates that God swore by His Throne of Glory that an Amalekite who comes to convert should not be accepted. According to this position, Haman’s descendants were only allowed to teach Torah in Bnei Brak – as the Sages attest – as the result of an error: A rabbinical court accepted a convert without knowing that he is a descendant of Amalek. Alternatively, an Amalekite descendant of the wicked Haman raped a Jewish woman, and those Torah teachers from Bnei Brak descended from her son, who was considered Jewish.

(6) *NOT TRANSLATED IN THE ORIGINAL* In conclusion, the best way to fulfill the mitzvah of eradicating Amalek is by inspiring them to do teshuvah. If they don't do teshuvah, another way that is also ideal, is to eradicate them in war. In actuality the mitzvah was fulfilled in a less ideal way: after many years their descendants dispersed and were swallowed up among the other nations, and any trace of them was lost. Their status of "Amalek" was thus rendered functionally extinct without them doing teshuvah.