Son of Sir Robert Steuart (1643-1707), 1st of Allanbank, and Helen Cockburn. Provost (1744-1745) of, and MP for, Edinburgh at the time of the Jacobite rebellion in 1745. He refused to arm the city, making it possible for the Jacobite Highland army to occupy it. In 1747 he was tried for neglect of duty and misbehaviour in the execution of his office. The trial was much publicised, and David Hume wrote a 51p pamphlet in his defence. He was acquitted and subsequently moved his business to London.
Boswell mentions him being present at a dinner party at John Trotter's in London on May 19, 1763.
Several writings were published concerning Stewart's trial in 1747, and a search on the AbeBooks used books search engine for The Trial of Archibald Stewart, should amount to some relevant hits. Sometimes it is even possible to find original copies of David Hume's A True Account of the Behaviour and Conduct of Archibald Stewart.