First, there should be one ribbon for every two players. (Make sure you have an even number of players.)
In your hand, hold a bunch of the ribbons from the middle so the ends dangle loose.
Have every participant grab the end of one ribbon. Let go of the ribbons, and the two people who are holding onto the same ribbon become dance partners.
This fun icebreaker helps mix up the dance floor and makes for some funny pairings (two male dancers/two female dancers!).