Green’s Dictionary of Slang

gee n.5

[abbr.]

(US tramp) a glass of alcohol.

[US]Irwin Amer. Tramp and Und. Sl. 84: GEE. – A glass of liquor; a gallon, especially when alcohol or liquor in large quantities is referred to.
[US]Ragen & Finston World’s Toughest Prison 800: gee – A glass of liquor.