Green’s Dictionary of Slang

1. a drunken party.

1976		R. Price Blood Brothers 6: Last week [...] the Mount rented out club D’Artagnan for a shit-face.
1992		R. Price Clockers 141: The Fury, two hours into a shitface, sat three tables away.

2. a drunkard.

2008

R. Price Lush Life 82: I certainly don’t want to turn up at my own place of business with some shitface already dragging his toes .