Described as a man of great learning and integrity,[2] Roberton matriculated at the University of Glasgow in March 1605 and graduated M.A.
[3][4] He passed as advocate and was appointed a judge of the Admiralty Court and a Justice-Deputy in 1626, a position he held without fee from 1626 to 1637.
Upon the Restoration Roberton was appointed judge and made an ordinary Lord of Session on 5 April 1661.
He petitioned the court their indulgence regarding his age and sickness for his non-attendance, asserting he had no scruples with the covenant.
Roberton's sister Margaret married Scottish professor of divinity David Dickson.