Green’s Dictionary of Slang

1. (US) a waste of time, a lightweight matter.

1929		C. Coe Hooch! 62: This bootleggin’ ain’t goin’ to be a ring-around-the-rosie. There’s too much money at stake.
1960		C. Cooper Jr Syndicate (1998) 3: I [...] don’t like to play ring-around-the-rosie.

2. (US gay) an orgy.

1972

B. Rodgers Queens’ Vernacular 59: an orgy of men; men linked anus-to-penis, anus-to-penis simultaneously [...] ring around the rosey.