A special election was held in January 19–20, 1795 to fill a vacancy left by Representative-elect John Barnwell (F) declining to serve the term for which he'd been elected.
| Candidate | Party | Votes[1] | Percent | ||
|---|---|---|---|---|---|
| Wade Hampton | Democratic-Republican | 198 | 29.3% | ||
| William Thompson | [2] | 176 | 26.0% | ||
| John Rutledge, Jr. | Federalist | 160 | 23.7% | ||
| William Elliot | 140 | 20.7% | |||
| Andrew Hartley | 2 | 0.3% |