No.
Rats generally don't carry the rabies virus. If your dog is vaccinated, he should be fine. Rats do however carry plenty of other . Things to look out are things like fleas and ticks which themselves transmit diseases from the rat to your dog.
here are some links from the cdc:
direct from rodents
http://www.cdc.gov/rodents/diseases/direct_rodents.htm
indirect from rodents
http://www.cdc.gov/rodents/diseases/...ct_rodents.htm