Promoted to captain on 31 January 1774, Dickson was given command of the fourth-rate HMS "Antelope" in January 1774 and the sixth-rate HMS "Greyhound" in October 1775. In Greyhound, he took part in the action against the Penobscot Expedition in July 1779 and fought at the Battle of Martinique in April 1780 during the American Revolutionary War. He was next given command of the third-rate HMS "Dublin" and saw action at the Battle of Cape Spartel in October 1782. After that he was given command of the third-rate HMS "Goliath" in 1786, of the third-rate HMS "Captain" in 1790 and the third-rate HMS "Egmont" in 1793.