The younger son of Harry Ord, of the king's remembrancer's office, by Anne, daughter of Francis Hutchinson of Barnard Castle, County Durham, he was born in London in 1756; his uncle, Robert Ord, was Chief Baron of the Scottish Exchequer.
Ord was elected a Fellow of the Society of Antiquaries of London on 26 January 1775, and of the Royal Society on 3 May 1787.