1929, "drunk," past participle adjective from piss (v.). From 1946 as "angry," from piss off.
piss
v.
late 13c., from Old French pissier "urinate" (12c.), from Vulgar Latin *pissiare, of imitative origin. To piss away (money, etc.) is from 1948. Related: Pissed; pissing. Pissing while (1550s) once meant "a short time."
He shall not piss my money against the wall; he shall not have my money to spend in liquor. ["Dictionary of Buckish Slang, University Wit and Pickpocket Eloquence," London, 1811]
piss
n.
late 14c., from piss (v.). As a pure intensifier (piss-poor, piss-ugly, etc.) it dates from World War II. Piss and vinegar first attested 1942. Piss-prophet "one who diagnosed diseases by inspection of urine" is attested from 1620s. Piss proud "erect upon awakening" is attested from 1796.