James was born on May 8, 1786 in Charleston, South Carolina to James and Elizabeth (Lynch) Hamilton. He practiced law in Charleston, and for several years served the city as its mayor. He was elected to the South Carolina state House of Representatives, and served from 1819 until 1822. When William Lowndes resigned from the U.S. Congress, Hamilton was elected to complete his term, and started his congressional career on December 13, 1822. He was re-elected in 1824 and 1826. He was a States' Rights Democrat.

Hamilton personally loaned $216,000 to the young Republic of Texas, and arranged other loans for them from the Bank of the United States. He served as a special agent for them in Europe, gaining diplomatic recognition for the new republic from Great Britain and Holland. He finally moved to Texas in 1855.

In 1857, while returning to Texas from Washington, D.C., Hamilton’s steam-boat was sunk, and he drowned in the Gulf of Mexico, reportedly after yielding his seat in a lifeboat to a woman and her child. Hamilton County, Texas is named in his honor.