Swinton's father had become a Quaker, was an active politician during the Protectorate, and had had his estates forfeited at the Restoration.
He succeeded his elder brother as head of the family in 1687 and returned to Scotland at the time of the Glorious Revolution, of which his uncle Lord Mersington was a supporter.
In 1689 he was appointed a commissioner of supply for Berwickshire, and the following year he was restored to his father's estates.
Swinton supported the Act of Union 1707, and was one of the Scottish representatives to the first Parliament of Great Britain and a commissioner of the Equivalent.
His wife died in about 1690, and he was married secondly on 17 February 1698 to Anne, daughter of Sir Robert Sinclair, 1st Baronet of Longformacus.