Green’s Dictionary of Slang

(US) a look; usu. in phr. get/take a hinge, to look at.

1940		J.H. O’Hara Pal Joey 112: It is a good thing I only write you letters instead of getting a hinge at your holy kisser.
1940		R.L. Bellem ‘Death’s Passport’ in Goodstone Pulps (1970) 112/2: Everybody wanted a hinge at the hero.
1943		R.L. Bellem ‘Half-Size Homicide’ in Speed Detective Nov. 🌐 I copped a hinge at him in my mirror.
1945		R.L. Bellem ‘Coffin for a Coward’ in Hollywood Detective Dec. 🌐 ‘Oh-h-h . . . you!’ she gasped as she got a hinge at my map.
1947		B. Schulberg Harder They Fall (1971) 20: I took a dutiful hinge at it [i.e. a photograph]. [Ibid.] 125: I saw how the boys instinctively turned for a hinge of the gams as she went past.
1955		B. Schulberg On the Waterfront (1964) 145: This priest [...] took a hinge at the shape this morning.
1971		T. Thackrey Thief 197: I just had to get another hinge at this lawyer-nut to see if he was for real.