Wanton was born to Governor Joseph Wanton and Mary Winthrop Wanton of Newport on February 8, 1730. Wanton graduated from Harvard University in 1751 and was involved with privateers during the French and Indian War possibly where he attained the title of colonel. Wanton's wife Abigail died in 1771. Wanton was elected Deputy Governor of Rhode Island in 1764 and 1767.
Wanton was a loyalist during the American Revolution and was accused of treason and imprisoned by Rhode Island General William West while the British occupied Narragansett Bay in 1776. Wanton's property (Hunter House) was confiscated, and he fled Newport when the Americans reoccupied the city in 1780. Joseph Wanton, Jr. was a vestryman at Trinity Church (Newport). Some genealogists speculate that he later became an Episcopal minister near Liverpool, England, although this seems inconsistent with other information about his life.