My icemaker came with a plastic tube and the water supply to the previous icemaker used copper tubing... is there a way of connecting the two...

Hi Bonnie...

Sure is a way to connect the two... ;)

You'll need to go to home depot and you'll want to pick up a 1/4" brass compression coupling/union fitting... (first image). Then you'll try to reuse the old copper nut (2nd image) and ferrule (3rd image) on the old copper line and the new plastic nut/ferrule provided at the plastic refrigerator line and screw them into the new compression coupling. This means that, for now, set aside the brass nuts/ferrules that come with the compression coupling and connect the two existing lines/fittings directly to the compression coupling itself. Do not use pipe dope or teflon tape here... simply screw the fittings into the coupling... tighten pretty tight without overdoing it.

Then check for leaks... hopefully, all set!

If not, then your plastic water line might require a compression INSERT (last image), or you may need to install a new nut/ferrule, but if so, pop back and discuss with us to determine next steps... OK?

Glad to help...

Mark