Green’s Dictionary of Slang

bird of the game n.

a prostitute.

1614		Jonson Bartholomew Fair IV v: Here will be ’Zekiel Edgworth, and three or four gallants [...] and I ha’ neither plover nor quail for ’em: persuade this between you two, to become a bird o’ the game.
c.1800		‘Jenny Macraw’ in Burns Merry Muses of Caledonia (1965) 169: Jenny Macraw was a bird o’ the game, / An’ mony a shot had been lows’d at her wame.