Charlton was born in Savannah, Georgia on January 19, 1807. A lawyer by training, Charlton served in various positions at the city and state level in addition to his U.S. Senate term. He was a member of the Georgia House of Representatives (1828), and he was appointed and subsequently elected a judge of the Eastern Circuit of Georgia in 1832. Charlton was also appointed as a United States District Attorney.

He was appointed as a Democrat to the United States Senate to fill the vacancy caused by the resignation of John Macpherson Berrien. Charlton served as the mayor of Savannah from 1839 to 1841. The father of Robert Charlton, Thomas U.P. Charlton, had previously served as the appointed mayor of Savannah in 1815 and again in 1819.

In 1829 Robert Charlton married Margaret Shick. Charlton ward, Savannah and Charlton County, Georgia are named after him. Charlton died in Savannah on January 18, 1854 and is buried in Laurel Grove Cemetery in that city.