Just yesterday I started singing this as an (American) friend and I played Scrabble. She'd never heard of it! It seems to be mostly a 'Canadian' thing, as I'm from Ladysmith, BC.
As I recall it went something like this (and yes, my mother taught it to us kids)(very catchy tune, too!)

There was a man
And his name was Rang
Rang-A-Pang-A-Tang.
His legs were long
And his feet were small
This China man could not walk at all.
ChickALaOhNo
China Man!