Arthur Dobbs was High Sheriff of Antrim in 1720 and in 1727 was returned for Carrickfergus in the Irish Parliament of 1727-1730. He was appointed Engineer-in-Chief and Surveyor-General in Ireland by Sir Robert Walpole.
In 1730 he commisioned the building of Castle Dobbs, Carrickfergus.
He was appointed Governor of North Carolina in 1754 and died there on 28 March 1765.