Green’s Dictionary of Slang

(US) a Model-A Ford automobile, first produced in 1927.

[1975		T. Berger Sneaky People (1980) 84: Buddy was about to get into the old A-model].
1986		S. King It (1987) 272: And when the A was finally running, he’d say that next year he was going to trade it for a Chevrolet.