(ו) הַכּוֹתֵב כְּתֹבֶת קַעֲקַע, כָּתַב וְלֹא קִעֲקַע, קִעֲקַע וְלֹא כָתַב, אֵינוֹ חַיָּב, עַד שֶׁיִּכְתֹּב וִיקַעֲקֵעַ בִּדְיוֹ וּבִכְחֹל וּבְכָל דָּבָר שֶׁהוּא רוֹשֵׁם. רַבִּי שִׁמְעוֹן בֶּן יְהוּדָה מִשּׁוּם רַבִּי שִׁמְעוֹן אוֹמֵר, אֵינוֹ חַיָּב עַד שֶׁיִּכְתּוֹב שָׁם הַשֵּׁם, שֶׁנֶּאֱמַר (ויקרא יט) וּכְתֹבֶת קַעֲקַע לֹא תִתְּנוּ בָּכֶם אֲנִי ה':
(6) One who tatoos: If he writes without engraving, or he engraves without writing, he is not liable for lashes, until he writes and engraves with ink or pigment or anything that leaves an impression. Rebbi Shimon ben Yehudah said in the name of Rebbi Shimon [bar Yochai]: He is not liable until he writes a name [of idolatry] there. As it says (Vayikra 19): "Do not tatoo yourself, for I am G-d."
מתני׳ הכותב כתובת קעקע כתב ולא קעקע קעקע ולא כתב אינו חייב עד שיכתוב ויקעקע בידו ובכחול ובכל דבר שהוא רושם ר"ש בן יהודה משום ר' שמעון אומר אינו חייב עד שיכתוב שם את השם שנאמר (ויקרא יט, כח) וכתובת קעקע לא תתנו בכם אני ה':
גמ׳ אמר ליה רב אחא בריה דרבא לרב אשי עד דיכתוב אני ה' ממש אמר ליה לא כדתני בר קפרא אינו חייב עד שיכתוב שם עבודת כוכבים שנאמר וכתובת קעקע לא תתנו בכם אני ה' אני ה' ולא אחר:
MISHNA: One who imprints a tattoo, by inserting a dye into recesses carved in the skin, is also liable to receive lashes. If one imprinted on the skin with a dye but did not carve the skin, or if one carved the skin but did not imprint the tattoo by adding a dye, he is not liable; he is not liable until he imprints and carves the skin, with ink, or with kohl [keḥol], or with any substance that marks. Rabbi Shimon ben Yehuda says in the name of Rabbi Shimon: He is liable only if he writes the name there, as it is stated: “And a tattoo inscription you shall not place upon you, I am the Lord” (Leviticus 19:28).
GEMARA: Rav Aḥa, son of Rava, said to Rav Ashi: Is Rabbi Shimon saying that one is liable only if he actually inscribes the words “I am the Lord” in his skin? Rav Ashi said to him: No, he is saying as bar Kappara teaches: One is liable only if he inscribes a name of an object of idol worship, as it is stated: “And a tattoo inscription you shall not place upon you, I am the Lord,” which means: Do not place an idolatrous name on your skin, as I am the Lord, and no one else.
Chabad:
The human body is G‑d’s creation, and it is therefore unbefitting to mutilate G‑d’s handiwork. It is especially unbefitting for members of G‑d’s chosen nation to mutilate their bodies. One must believe that G‑d, the greatest artisan of all, formed him or her in the most fitting way, and one must not change this form. Changing one’s body (unless it is for health reasons) is tantamount to insulting G‑d’s handiwork.
In ancient times, it was customary for idol-worshippers to tattoo themselves as a sign of commitment to their deity—much like an animal that is branded by its owner. On many occasions the Torah forbids practices that emulate pagan customs, considering that following their traditions is the first step towards subscribing to their idolatrous beliefs and services.
The covenant of circumcision is unique in its being a sign in our bodies of our relationship with G‑d. Making other signs in one’s body would weaken and cheapen this special sign.
Burial
The Torah forbids us from tattooing our bodies. Nonetheless, one who has had tattoos can still buried in a Jewish cemetery.
That said, every Jewish burial society has the right to enact its own criteria for who may and may not be buried in their plot. This stems from people’s desire (or right?) to be buried in proximity to others of their choosing. So while technically there is nothing in Jewish law which prohibits a tattooed person from being interred in a Jewish cemetery, certain burial societies—not the majority of them, or even close—will not bury among their own a person who willingly tattooed him- or herself, as it is a permanent exhibition of violation of Jewish Law.
This practice by certain burial societies led to the common misconception that this ban was an inherent part of Jewish law.
NY Times
But the edict isn’t true. The eight rabbinical scholars interviewed for this article, from institutions like the Jewish Theological Seminary and Yeshiva University, said it’s an urban legend, most likely started because a specific cemetery had a policy against tattoos. Jewish parents and grandparents picked up on it and over time, their distaste for tattoos was presented as scriptural doctrine.