Pinckney was born in Charleston, South Carolina, and was educated in Great Britain and France. He fought in the American Revolutionary War from 1775 to 1781. Pinckney was governor of South Carolina from 1787 to 1789 and became the U.S. ambassador to Great Britain in 1792. He was a member of the United States House of Representatives from 1797 to 1801.
His brother Charles Cotesworth Pinckney and his cousin Governor Charles Pinckney were signers of the United States Constitution. He arranged the Treaty of San Lorenzo, also known as the Pinckney's Treaty, with Spain in 1795 . He ran as a Federalist candidate in the U.S. presidential election, 1796.