Armie Hammer Says 'Birth' Fan Got Screwed

'Birth of a Nation' star Armie Hammer smells a rat -- a racist one -- when it comes to the treatment one moviegoer claims he got when he tried to buy a ticket for the flick.

Armie told us he saw the Facebook video posted by a guy in Delaware -- he claims the box office at a Regal Cinema told him 'Birth' was sold-out, but then he went inside and found the theater almost completely empty.

As we first reported ... Regal denies any wrongdoing or racism -- but Armie's not totally convinced, and says he would've flipped out way more than this guy did.