A slang term meaning annoyed, angry, irritable, cranky, splenetic, or bad-tempered, as in "Don't get shirty with me; it's not my fault." Apparently a synonym is snorty, though I've never heard that term before.
The etymology is apparently uncertain, but shirty may derive from the expression "to get someone's shirt out", meaning to annoy or irritate them; or perhaps as the opposite of "keeping your shirt on", meaning don't get annoyed.