Rig-a-Jig-Jig is a popular nineteenth-century folk song where a young man encounters a pretty girl.
[1] It is useful for singing games since it is a familiar tune that can be used by activity leaders even if there are no available musicians.
A "young man" then moves inside the circle while singing the song.
If the pretty lady sings "a nice young man" then they join hands in the chorus and move together.
The process is repeated with a new young man until all players are partnered.