1742-91. He was the son of Dr William Robertson of Richmond, Surrey, and of his wife, Mary Seton.
Robertson was commissioned lieutenant on 5 March 1762 and promoted commander on 4 November 1778. He commissioned the newly purchased fireship Incendiary 8 for the Western Squadron and retained her until the late summer of the following year. He then joined the fireship Firebrand 16 in March 1780, serving with the Channel fleet and participating in the Relief of Gibraltar on 12 April 1781.
He fought at the Battle of the Doggersbank on 5 August 1781 flying the flag of Vice-Admiral Hyde Parker aboard the Fortitude 74, which ship suffered casualties of twenty men killed and sixty-seven wounded, and was posted captain on 15 August. After joining the Buffalo 60 he was at Sheerness in the autumn and retained her into 1782 before moving to the Danae 32 and going out to Newfoundland in June. Here he captured the American privateer Tiger on 27 August beforethe Danae was eventually paid off in February 1783.
Robertson recommissioned the aged Aeolus 32 in April 1783, going out to Newfoundland and paying her off at Chatham in January 1784. He then took the newly commissioned Thisbe 28 out to Newfoundland in the following month and thereafter served on that station for three years.
He died on 21 November 1791 at Kenilworth, Warwickshire.
Robertson married Ann Lewis of Philadelphia, USA, and had issue three daughters and a son.