The film isn't much help. All we're told is that he's
Captain Steve Trevor… Pilot… American Expeditionary Force.
and that he's working on secondment for British Intelligence. This doesn't actually confirm his nationality, merely who he's working for.
Luckily, the omniscient narrator in the film's novelisation is kind enough to give us proof of his background.
While Diana watched, the others helped themselves to guns. It pleased
her that she could recognize them too. Sammy grabbed a Lee–Enfield
Mark VII, .303 caliber. And Steve, the American, picked up an American
gun, a Winchester 12-gauge repeating shotgun. Thanks to Steve, she
also knew their magazine capacities and effective firing ranges.
Wonder Woman: Official Movie Novelisation