Son of Robert Arbuthnot (1694?-1756), 1st Baronet of Haddo-Rattray, and Mary Petrie (1695?-1756). Married (1759) to Mary Urquhart (1745-1818), with whom he had four children, Robert (1760-1809), Elizabeth (1765-1841)1, George (1772-1843)2 and William (1766-1829).3
Arbuthnot was a merchant in Peterhead, before moving to Edinburgh at some time before 1772, settling as a banker. He was for many years Secretary of the Board of Trustees for the Encouragement of the Manufacturers and Fisheries of Scotland, retaining the position until his death in 1803. He was succeeded in this position by his son William.
He was possessed of a genial and attractive disposition, and he counted among his friends the poet and philosopher James Beattie, as well as Sir Robert Murray Keith, British Ambassador in Vienna.4
Boswell presented Arbuthnot to Dr Johnson in Edinburgh on August 15, 1773, a few days before Johnson and Boswell set out on their tour of Scotland and the Hebrides. Boswell wrote of him, in Journal of a Tour to the Hebrides, that he was "a relation of the celebrated Dr. Arbuthnot, and a man of literature and taste. To him we were obliged for a previous recommendation which secured us a very agreeable reception at St. Andrews, and which Dr. Johnson in his Journey5 ascribes to "some invisible friend"."