I didn't notice whether he wore one or not to tell the truth. Good spot though and an interesting point. I guess it wasn't really Michaels character to wear one, they're usually worn by the flashy flamboyant people like the Gotti's of this world. It seems wierd he'd wear one in Part III though and probably only done as a Mafia stereotype.
I'm pretty sure he wasn't wearing one in The Godfather or in pt. II but I think he was wearing a silver or platinum pinky ring on his right hand in pt. III except for one scene where he was wearing it on his left hand I believe.