Green’s Dictionary of Slang

1. a hand; a fist.

1919		D. Runyon in Pittsburg Press (PA) 27 June 14/4: Taking a jaunt to gay Paree [...] and firing a ‘Mary Ann’ at Georges Carpentier and some of the other lads.
1925		T.A. Dorgan in Zwilling TAD Lex. (1993) 56: Now Buck, soon as de bell sings swing old Mary Ann right on dat palooka’s button.
1949		Monteleone Criminal Sl. (rev. edn) 153: mary ann A knockout blow.
1960		J. Franklyn Dict. of Rhy. Sl.
1972		Dodson & Saczek Dict. of Cockney Rhy. Sl.

2. a fan.

1992

R. Puxley Cockney Rabbit.