Green’s Dictionary of Slang

rummy adj.²

drunken.

1830		Ely’s Hawk & Buzzard (NY) 26 June 4/2: In the habit of going to Hoboken [...] for the purpose of getting rummy and insulting respectable people.
1842		Nichols’ Wkly Arena (NY) 4 June n.p.: One of our most conspicuous characters — conspicuous alike in the brothel and the bar-room [...] ‘Rummy Jack’.
1850		Life in Boston & N.Y. (Boston, MA) 10 Aug. n.p.: A band consisting of himself, Old nell, Rummy B., and long-legged Hay-pole.
1918		implied in rummy stiff
1921		Broadway Brevities Dec. 43/1: As soon as this rummy Romeo notices that, the bets will be off and he'll be home at the dinner-table again!
1952		J. Jones From Here to Eternity (1998) 33: They were always shocked, even the rummy barflies.
1969		J. Crumley One to Count Cadence (1987) 82: You’re not some rummy old sergeant who thinks the Army is his mother.
1985		(con. 1936) F. Deford Sports Illus. June 🌐 ‘You rummy Jew bastard’.

In compounds

rummy stiff (n.) [stiff n.¹ (5a)]

(US tramp) an alcoholic tramp.

1918

‘A-No. 1’ Mother of the Hoboes 44: The Rating Of The Tramps 29 Rummy Stiff: deranged intellect by habitual use of raw rum.