This question got asked on another turtle forum I'm on and I searched and searched for the answer online.
As far as I could find information, I'd say no, your turtle can't get ick. The member who had the ick problem also rang her vet and he said no, turtle's cannot get ick.
To get rid of the ick, though, you'll need to remove all the fish from your turtle tank and put them in another one. Then the ick in the turtle tank won't have a chance to infect any other hosts (fish) and will eventually die off.
If you want to cure the sick fish, you can slowly raise the water temps up to 80F or buy ick medicine from your pet shop, but the best way to get the ick out of your turtle tank is to remove all the fish and put them in a separate tank.
A good article on it can be found
here.