Now, that's almost creepy. There is a German movie that's fits perfectly. Two guys doing some kind of criminal carrier service, one gets wounded at one job, from the scratch grows a tattoo, turns out he is infected by demon blood or something and turns into one. Lots of coats an fighting in dark muddy places and stuff.
BUT: the movie is not out yet. It's scheduled for end of this month, title being "Bloodbound". A trailer can be seen here (down at the right side): http://www.myspace.com/bloodboundderfilm
So, I guess this one is not it. There is a another Asian movie with a growing tattoo, called "Ashura - The Demon Slayer". But that one is pretty recent, too. And it is a woman, that has the tattoo.