Green’s Dictionary of Slang

1. an honest, trustworthy person.

1914		Jackson & Hellyer Vocab. Criminal Sl. 79: square-shooter [...] a dependable person; a reliable, compact-keeping person.
1927		‘Max Brand’ Pleasant Jim 109: You always was considered a square-shooter and a fair one.
1933		‘Goat’ Laven Rough Stuff 181: Inside the prison walls there is a city by itself, and you meet all types of people there; square shooters, and rats as low as a snake’s belly.
1942		R.L. Bellem ‘Daughter of Murder’ Dan Turner – Hollywood Detective Dec. 🌐 This Jarrett guy was one of the biggest legal moguls in the cinema colony [...] He was a square shooter.
1956		‘Ed Lacy’ Men from the Boys (1967) 16: He looks like a square shooter, competent.
1960		A. Buzo Front Room Boys Scene v: I’ve got a lot of time for Hendo, he’s a square-shooter.
1975		T. Berger Sneaky People (1980) 88: You’ve always been a squareshooter.
2007		P.S. Powers Pulp Writer 99: But he was too honest for that; he was a square shooter.

2. one who espouses a respectable (as opposed to criminal) life.

1928

J. Callahan Man’s Grim Justice 126: ‘I’m through with the racket for the rest of me loife.’ Billy laughed at him. [...] ‘You’ll never be a square-shooter.’.