Barker was commissioned lieutenant on 6 November 1777 and promoted commander on 1 December 1787 after commissioning the newly launched St. George 98 for the Dutch Armament, although this vessel was paid off as incomplete that month.
By the early days of the French Revolutionary War, he was commanding the sloop Shark, which vessel underwent a refit at Portsmouth in February 1793 before bringing a valuable French prize brig into that port in the following month. During the early summer she went out to Newfoundland with a convoy, but having parted from her charges within the week she was presumed lost. In September however, she returned to Portsmouth from Newfoundland with news of the death of Captain George William Augustus Courtenay of the Boston 32 in action with the French frigate Embuscade on 31 July off New York.
Barker was posted captain of the twenty-year-old frigate Triton 28 on 10 October 1793, seeing service in convoy duty to Ireland, and sailing for Jamaica in March 1795 with a convoy before returning to Portsmouth in August with the homeward-bound convoy. Whilst in the West Indies a fever ravaged through the frigate, and by the time she reached home up to a third of her crew had died. In October the Triton sailed with a convoy for the Downs, and she was decommissioned and broken up in the following year.
During the summer of 1796 Barker commissioned the twelve-pounder French prize Tribune 36, in which he departed England with a convoy for Newfoundland and Quebec in September 1797. After becoming detached from her charges in mid-Atlantic, the Tribune arrived at Halifax, Nova Scotia, on 16 November where Barker was advised by the sailing master that he could take the vessel into harbour with the help of a local Negro, thereby negating the need of a pilot. Unfortunately, the Tribune drove ashore with the loss of her rudder, and despite the protestations of a local guard officer who came aboard to state that the frigate was doomed, Captain Barker determined to save her. After heaving the guns overboard and cutting away the mizzenmast the frigate came off the shoal, but as had been predicted by the guard officer a winter gale sprang up from the east, and with the Tribune unable to steer, she foundered near the shore in the rocky Herring Cove at 10.30 p.m. Captain Barker and two hundred men were lost immediately, and a further one hundred died when the mainmast, to which they had been clinging, fell away at midnight. A mere dozen men survived.
Barker married Mary Shugar of Portsmouth on 30 Apr 1788. The address in his will was given as Southwick, Hampshire, whilst he earlier lived at Portsea.