Green’s Dictionary of Slang

(US, usu. juv.) a claim, esp. a claim of first rights to something.

1939

R.I. McDavid Jr ‘Citadel Gloss.’ in AS XIV:1 26: Ducks, n., with verbal force. 1. Request for a portion of a cigarette, candy bar, etc., after the owner has had enough. 2. Request for the use of an article after the owner is through, as ‘Ducks on your electric razor.’.