I have gas/hot water heating system with radiators. I want to replace the iron pipe mains with copper tubing and adapt to the iron risers going up to the radiators. Is there a fitting to adapt unthreaded iron pipe to copper?

You would need to use dielectric unions. Plumbing System Components - The Dielectric Union
This would prevent the corrosion that would happen with these two dissimilar metals.

Thank you ballengerb1. The dielectric union will solve part of my problem. I am more interested inknowing if there is an adpter for copper to unthreaded iron pipe. The risers leading up to the radiators hang too low in the basement. I would like to just cut them at ceiling height and adapt to new copper there. I want to avoid either replacing the risers with shorter nipples or cutting and re-threading the risers.

Sorry, don't know of a good away around your situation. The unions I've used would require rethreading the galvanized pipe but that's no big issue for me because I have the tools. You can rent the equipment for a few hours for about $15. Obviously the copper side of the union can be soldered.

Maybe check out the Shark-Bite connectors. I think the 3/4'' ones would join 3/4'' copper to unthreaded 1/2'' iron. Check the directions. Ace Hardware has them plus plumbing supplies. I haven't seen them at the big box stores.