Yes. Ice is solid water; so of course your dog can eat ice!
There is a myth of your dog suffering from bloat if given ice or ice water.
Bloat definitely exists (if you give a hot, overheated dog too much water he can swallow too much air) and can be very serious, but just consuming ice or ice water will not put your dog at risk. Just monitor his water intake after heavy exercise or let him cool off a bit before giving him water.
Also, supervise your dog if you give him an ice cube, as he may swallow it whole and choke on it.