(28) You shall not make gashes in your flesh for the dead, nor incise any marks on yourselves: I am the L-RD.
(ו) הכותב כתבת קעקע, כתב ולא קעקע, קעקע ולא כתב, אינו חיב עד שיכתוב ויקעקע בדיו ובכחול ובכל דבר שהוא רושם. רבי שמעון בן יהודה משום רבי שמעון אומר: אינו חיב עד שיכתוב שם השם, שנאמר (ויקרא יט) וכתבת קעקע לא תתנו בכם אני ה'.
(6) With regard to one who tattoos his skin, [if] he made a mark [an incision in his skin] but did not tattoo in it [that is, did not fill it in with ink, or] tattooed in it [that is, made ink marks on the surface of his skin] but did not make a mar [so that the process of tattooing was not completed] -- he is not liable. He is liable [only] when he marks and tattoos with ink or eye paint or anything that leaves a [permanent] mark. Rabbi Simon ben Judah says in the name of Rabbi Simon, 'He is liable only when he writes the name of G-d,' as it is written in the Torah Leviticus 10: Do not incise any marks on yourselves: I am the L-RD."
ואינו חייב עד שיכתוב ויקעקע בדיו ובכחול לעבודה זרה.
Tosefta Makkot 4:15
And one is not liable (for punishment) until one writes and incises with dye or blue for the purpose of idol worship.
[יא] "כְּתֹבֶת קַעֲקַע" (ויקרא יט,כח) הָאֲמוּרָה בַּתּוֹרָה, הוּא שֶׁיִּשְׂרֹט עַל בְּשָׂרוֹ וִימַלֵּא מְקוֹם הַשְּׂרִיטָה כֹּחַל אוֹ דְּיוֹ אוֹ שְׁאָר צִבְעוֹנִין הָרוֹשְׁמִין; וְזֶה הָיָה מִנְהַג הַגּוֹיִים שֶׁרוֹשְׁמִין עַצְמָן לַעֲבוֹדָה זָרָה שֶׁלָּהֶן, כְּלוֹמַר שְׁהוּא עֶבֶד מָכוּר לָהּ וּמֻרְשָׁם לַעֲבוֹדָתָהּ.
וּמֵעֵת שֶׁיִּרְשֹׁם בְּאֶחָד מִדְּבָרִים הָרוֹשְׁמִים אַחַר שֶׁיִּשְׂרֹט, בְּאֵי זֶה מָקוֹם מִן הַגּוּף, בֵּין אִישׁ בֵּין אִשָּׁה--לוֹקֶה.
כָּתַב וְלֹא רָשַׁם בִּצְבָע, אוֹ שֶׁרָשַׁם בִּצְבָע וְלֹא כָתַב בִּשְׂרִיטָה--פָּטוּר: עַד שֶׁיִּכְתֹּב וִיקַעְקַע, שֶׁנֶּאֱמָר "וּכְתֹבֶת קַעֲקַע" (ויקרא יט,כח).
בַּמֶּה דְּבָרִים אֲמוּרִים, בְּכוֹתֵב. אֲבָל זֶה שֶׁכָּתְבוּ בִּבְשָׂרוֹ וְקִעְקְעוּ בּוֹ--אֵינוּ חַיָּב אֵלָא אִם סִיַּע, כְּדֵי שֶׁיֵּעָשֶׂה מַעֲשֶׂה; אֲבָל אִם לֹא עָשָׂה כְּלוּם, אֵינוּ לוֹקֶה.
Maimonides, Mishneh Torah: Laws of Idolatry 12:11
"Incising a mark." The prohibition of tattooing that is biblically derived is making an incision in one's flesh and filling the incision with eye paint, ink, or any dye that leaves an imprint. This was the practice of idolaters who [permanently] marked their bodies for the sake of their idol worship. Basically, [they understood this to be] that they are likened to servants sold to the idol and designated to serve it.
When one makes an imprint with one of the substances [listed above], the punishment of lashes is carried out, whether it is a man or a woman.
If one wrote but did not dye, or dyed but did not write [by incising in the flesh] -- this person is not liable, as it is written (Lev. 19:28), "or incise any marks."
To whom does this [prohibition] apply? To the one who is performing the tattooing, but the one who is tattooed by others is not liable unless he helped the tattooer [so that it is] as if he tattooed too. However, if the one being tattooed did not perform the action, [the punishment] of lashes is not applied.
(ה) זֶ֤ה יֹאמַר֙ לַֽה' אָ֔נִי וְזֶ֖ה יִקְרָ֣א בְשֵֽׁם־יַעֲקֹ֑ב וְזֶ֗ה יִכְתֹּ֤ב יָדוֹ֙ לַֽה' וּבְשֵׁ֥ם יִשְׂרָאֵ֖ל יְכַנֶּֽה׃
(5) One shall say: ‘I am the L-RD’S’; And another shall call himself by the name of Jacob; And another shall mark his arm "of the L-rd's" and adopt the name of Israel.
(16) Behold, I have engraved you upon the palms of My hands; Your walls are continually before Me.
Rabbi Alan Lucas, Jewish Committee on Laws and Standards (Rabbinical Assembly of the United Synagogue of Conservative Judaism)
In our day, the prohibition against all forms of tattooing regardless of their intent, should be maintained. In addition to the fact that Judaism has a long history of distaste for tattoos, tattooing becomes even more distasteful in a contemporary secular society that is constantly challenging the Jewish concept that we are created b’tzelem Elokim (in the image of G-d) and that our bodies are to be viewed as a precious gift on loan from G-d, to be entrusted into our care and [are] not our personal property to do with as we choose. Voluntary tattooing even if not done for idolatrous purposes expresses a negation of this fundamental Jewish perspective.
As tattoos become more popular in contemporary society, there is a need to reinforce the prohibition against tattooing in our communities and counterbalance it with education regarding the traditional concept that we are created b’tzelem Elokim. But, however distasteful we may find the practice there is no basis for restricting burial to Jews who violate this prohibition or even limiting their participation in synagogue ritual. The fact that someone may have violated the laws of kashrut at some point in his or her life or violated the laws of Shabbat would not merit such sanctions; the prohibition against tattooing is certainly no worse. It is only because of the permanent nature of the tattoo that the transgression is still visible.
Joey Ramona, (Jewish, queer, feminist tattoo artist)
https://www.heyalma.com/joey-ramona-is-the-queer-jewish-tattoo-artist-of-our-dreams/
There are a few aspects to the practice that I think about, one being that our culture is centered around G-d and existing in the world as we are created, so the job that I do, my career, is part of who I am, and I don’t think that I should have to forgo that because of some archaic rules. Also, tattooing was used [in the Holocaust] to basically reduce the identity of Jews to a number. I think what I’m doing now is an attempt to subvert that, and putting Jewish images on your body permanently is a way of saying, “actually yes, I am Jewish. I’m not a number. I’m a person with all these different faucets, and I’m proud of who I am. And I’m proud of my Jewish identity.”