Assuming this is a character for PFS play, I'd say "no."
Feats which can be taken more than once state as much (see, e.g. Spell Focus, Spell Mastery, Weapon Focus, Alignment Channel, Extra Ki, Exotic Weapon Proficiency, etc.) and say what happens when you take it again (pick another spell school, pick 3 more spells, pick another weapon, pick another alignment, stacks with itself, pick another exotic weapon, etc.).
Varisian Tattoo does not state it can be taken multiple times, and does not say what it does when you take it again, thus by RAW (i.e. in PFS play) it cannot be taken multiple times (see Extra Channel for another example--most of the other "Extra" feats can be taken multiple times, but not Extra Channel!).
If you're running/playing in a home game, ask the GM. (or if an official jumps in here and says "Oh, yeah you're supposed to be able to take that multiple times" then you're set for PFS, but don't bet on that happening).
