PawtucketAuto dealer license in Rhode Island. Pawtucket is a city in Providence County, Rhode Island, USA. The population was 71 148 in 2010 census. And the fourth largest city in the state. Pawtucket was the major contributor to the cotton textile industry during the American Revolution. Slater Mill, built in 1793 by Samuel Slater, a Black River Falls in downtown Pawtucket, was the first fully mechanized cotton mill run in America.