According to the gemara in Makkos 21a, it seems that the biblical prohibition of tattoos only extends to tattoos made for religious purpose. However, the vast majority of poskim all seem to imply that there is at least a rabbinic prohibition of tattooing anything else. Where is the rabbinic prohibition recorded?
Mishnah Makkos 3:6 and Gemara 21a;
Yerushalmi Makkos 3:6
Rambam (Avodat Kochavim 12:11) and Shulchan Aruch (YD180:1; Shach 180:1) both rule that one has only done an aveira if one both pierces the skin and adds colour.