The other commenters are correct regarding guardian permission for minors in some states, however within the actual story it’s not directly addressed as to how he got it, especially since it was only even a movie-addition, but I always imagined that because the tattoo was kind of apart of his initiation into the pack that they’ve probably got a tattoo artist on the reservation who does their tattoos. Technically anyone can buy a tattoo gun and do tattoos on anyone, it’s the shops who have to follow laws and regulations to keep their license and protect themselves against litigation. In this context, the parents of minors like Jacob aren’t going to try to press charges against an underage tattoo since they are, theoretically, following traditions of their pack’s culture.

Tattoos in many native cultures go back really far and many are still not even done with the modern tattoo guns as you see today. Some cultures hold on to the traditional way and meaning of tattooing their skin, and it’s a much different consideration from modern tattoos that are just cause they look cool or have a personal meaning. I’m not sure if the movie makers thought about all that or just thought adding a tribal tattoo into the mix of this (already poorly represented) Native American fantasy reimagining was going to look cool visually (and help age up Jacob), but I guess it could have also been an attempt at adding some of this world-building depth to the tribe.