Green’s Dictionary of Slang

brown v.3

[brown n. (3a)]

1. [1920s] (US) used in a number of semi-euph. excl. e.g. I’ll be browned! brown me! [synon. with buggered adj.1 / bugger me! under bugger v.1 ].

2. [20C+] (orig. US, also do a brown) to perform anal intercourse, to sodomize.

In compounds

brown artist (n.) [-artist sfx]

[1950s+] a male homosexual who takes the active role in anal intercourse.

brown-hole (v.) [sense 2 above + hole n.1 (1a)]

[1980s+] (US gay) to have anal intercourse.