Tattoos are for unbelievers. God forbids them on His people.
Ye shall not make any cuttings in your flesh for the dead, nor print any marks upon you: I am the LORD. (Lev 19:28)
JOHN GILL'S COMMENTARY
...nor print any marks upon you;
Aben Ezra observes, there are some that say this is in connection with the preceding clause, for there were who marked their bodies with a known figure, by burning, for the dead; and he adds, and there are to this day such, who are marked in their youth in their faces, that they may be known; these prints or marks were made with ink or black lead, or, however, the incisions in the flesh were filled up therewith; but this was usually done as an idolatrous practice; so says Ben Gersom, this was the custom of the Gentiles in ancient times, to imprint upon themselves the mark of an idol, to show that they were his servants...
One only has to look at most tattoos to see that they have nothing edifying about them. So this is another worldly practice to be shunned by Christians.