Not only NO, but HELL NO.
Here's why--it's not the "Ewww, tattoos are gross" reason, or even the "Ewww, tattoos are STOOPID" reason...it's the "I HATE THIS TATTOO-=if YOU hadn't signed for it, I wouldn't HAVE IT. It's ALL YOUR FAULT!!!!!!!!" reason.
If people want to adorn their body, let them. But let them do it at an age where the decision is theirs, and THEIRS ALONE.
Eighteen is just around the corner. If he still wants it when he's eighteen, he can go get it, AND HE CAN PAY FOR IT.
Parents should be parents, not "fashion enablers." And that includes PAYING for tattoos--you want it, you pay for it yourself.