His parents were Henry Middleton and Mary Baker Williams. He was educated in Britain, at Westminster School, London, and St John's College, Cambridge. He studied law at the Middle Temple and traveled extensively in Europe where his taste in literature, music, and art was developed and refined. In 1764 Arthur and his bride Mary Izard settled at Middleton Place. (His wife was a cousin of South Carolina Congressman Ralph Izard; likewise a son of Congressman Izard was married to a niece of Arthur Middleton, and another son married Arthur's daughter Emma). Keenly interested in Carolina politics, Arthur Middleton was a more radical thinker than his father, Henry Middleton. He was a leader of the American Party in Carolina and one of the boldest members of the Council of Safety and its Secret Committee. In 1776, Arthur was elected to succeed his father in the Continental Congress and subsequently was a signer of the Declaration of Independence. Also in 1776 he and William Henry Drayton designed the Great Seal Of South Carolina. Despite the time he spent in England, his attitude toward Loyalists was said to be ruthless.
During the American Revolutionary War, Arthur served in the defense of Charleston. After the city's fall to the British in 1780, he was sent as a prisoner of war to St. Augustine, Florida (along with Edward Rutledge), until exchanged in July the following year.
Arthur died on January 1, 1787 at the age of 44. He was buried in the family tomb in the Gardens at Middleton Place. The plantation then passed to Henry, his eldest son, who went on to a career in politics. He was elected Governor of South Carolina (1810–1812), U.S. Representative (1815–1819), and held the post of Minister to Russia (1820–1830).
He was an ancestor of Baldur von Schirach, one time leader of the Hitler Youth and later Governor ("Gauleiter" or "Reichsstatthalter") of the Reichsgau Vienna who was convicted of "crimes against humanity" at the Nuremberg Trials, through Baldur Von Schirach's mother Emma Middleton Lynah Tillou (1872 – 1944). He was also the grandfather of actor Charles Middleton, who played Ming the Merciless in the Flash Gordon movies of the 1930s.