Green’s Dictionary of Slang

birdie n.¹

the penis.

1927		‘Jock McLaren’s Birdie’ in Immortalia 94: The kilt with the weather began to shrink, / Till it scarcely reached his heardie. / Then Jock was shocked one day to find / That na mair it covered his birdie.
1931		in Randolph & Legman ‘Unprintable’ Ozark Folksongs & Folklore’ II (1992).
1941		G. Legman ‘Lang. of Homosexuality’ Appendix VII in Henry Sex Variants.