Nick Cannon -- You Win, Mariah ... I'll Sign the Papers (AUDIO)

Nick Cannon is firing back at Mariah Carey for claiming he's dragging his feet on signing the divorce papers -- and he's doing it with a freestyle rap.

Nick dropped, "Divorce Papers" on SoundCloud -- it's a 4 minute rant about the divorce, his health and his child visitation rights. Check out the clip ... we gave you the highlights.

TMZ broke the story ... his divorce from Mariah's been hammered out on paper, but for some reason he just hasn't signed yet. On the track, Nick hints at a few reasons, like his health. He raps, he "almost died twice."

The silver lining for Mariah might be the closing line of the song. If we can believe his freestyle ... someone's about to get her walking papers.