No, Rhode Island is not a peninsula. Despite its name and extensive coastline, it's actually the smallest U.S. state by area (1,214 sq mi / 3,144 km²) and is classified as a state comprising mainland territory and numerous islands.
The name "Rhode Island" historically referred specifically to Aquidneck Island (where Newport and Middletown are located). The mainland settlements (Providence, Warwick, etc.) were originally the "Providence Plantations." The 1663 royal charter combined them as "Rhode Island and Providence Plantations"—a name retained until 2020 when voters removed "and Providence Plantations."
The state's extensive coastline (384 miles of tidal shoreline) and maritime character create a "peninsular feel" without meeting the geographic definition.