He studied law, was admitted to the bar in 1809, and commenced practice in Lancaster, Kentucky.
He served as chairman of the Committee on Private Land Claims (Fifteenth Congress).
He declined the appointment as Governor of Arkansas Territory tendered by President James Monroe and the diplomatic posts of United States Minister to Colombia in 1824 and to Peru in 1828.
Robertson was elected as a Whig a member of the Kentucky House of Representatives in 1848, 1851, and 1852, and served as speaker in the two last-named years.
Robertson's sister, Charlotte, was the second wife of Kentucky Governor Robert P. Letcher.