Can a half-elf raised by Varisian nomads take the trait Varisian Tattoo?
A half-elf can take human race traits
The Pathfinder Core Rulebook FAQ includes this exchange:
Half-Elf or Half-Orc: Can a character of either of these races select human racial archetypes (such as from Advanced Race Guide)?
Yes. Half-elves and half-orcs may select racial favored class options, archetypes, traits, and so on, as if they were a full member of both races (a half-elf can select elf and human rules elements, a half-orc can select human and orc rules elements).
- Edit 9/26/13: This is a reversal of an earlier ruling. This resolves a discrepancy between this FAQ and two Advanced Player's Guide FAQs.
(Emphasis and formatting mine.)
Half-elves count both as human and elf for any traits, feats, magic items or effects that work only on a certain race.
From the core rulebook:
Elf Blood: Half-elves count as both elves and humans for any effect related to race.