Green’s Dictionary of Slang

an invitation to take a drink.

1859		W. Kelly Life in Victoria I 166: Fill us a nobbler – dark; what’s yours, mate?
1890		Bulletin (Sydney) 9 Aug. 15/4: Chloe’s disquisitions on Dickens, always finishing up with ‘Whisky, did you say?’ are but a sweet memory. Literature, the Fine Arts, and the Public Service heard of the departure with a moment’s interest and then asked ‘What’s yours?’.
1902		Bulletin (Sydney) 9 Aug. 16/1: The Barmaid (to the station-hand): ‘And what’s yours?’ / The Dog-Stiffener: ‘Oh, something aboriginal. Gin or Boomerang.’.
1917		F. Packard Adventures of Jimmie Dale (1918) I vi: The man behind the bar [...] favoured him with a blank stare. ‘Never heard of de guy!’ he announced brusquely. ‘Wot’s yours?’.
1922		Joyce Ulysses 283: Give it a name, citizen, says Joe. – Wine of the country, says he. – What’s yours? says Joe.
1938		W. Watson Miss Pettigrew Lives For A Day (2000) 182: ‘What’s yours?’ asked Tony. ‘I will have,’ said Miss Pettigrew, ‘a small glass of sherry, thank you.’.
1947		H.C. Bosman Jacaranda in the Night (1981) I 299: We got to have a sundowner. What’s yours, dearie?
1955		Picture Post (ad for The Brewers’ Society) 23 July 22: What’s yours? Do you like a bitter?
1965		E. Bond Saved Scene x: pete (to Liz): Wass yourn, darlin’? [...] liz: could I ’ave a coffee?
1997		P. Theroux Kowloon Tong 84: ‘What’s yours?’ [...] He ordered a beer.