I didn't know he even had one. But ট্যাটু have been around for a long time, he might have gotten one when he was still human? I don't know for sure. It might have just been for the movie. Good find though, I'll have to watch twilight again to see it:)
He has two tattoos. The actor got tattooed when he was 16 years old. In Los Angeles, a few years later, he decided to add আরো to his tribal dragon on his arm and didn't like the finished result, so he has been working on getting the whole thing removed. His other tattoo, on his hip, says "Godspeed".
The producers probably just thought the tat was cool and decided not to cover it up.