Green’s Dictionary of Slang

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

1929		C. Coe Hooch! 62: This bootleggin’ ain’t goin’ to be a ring-around-the-rosie. There’s too much money at stake.
1952		W.R. Burnett Vanity Row 232: ‘All right. All right.’ Lynch spoke impatiently. ‘Let’s not get into ring-around-the-rosie’.
1956		‘James Updyke’ [W.R. Burnett] It’s Always Four O’Clock 134: [H]e didn’t like this ring-around-the-rosie underhand business at all.
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.