Alexander was born in London as the third son of John Ramsay, 13th Earl of Dalhousie, and his wife, Lady Ida Louisa Bennet, daughter of Charles Bennet, 6th Earl of Tankerville. He entered the Royal Navy as a cadet on HMS "Britannia" in 1894. He first went to sea on , the flagship of Admiral Sir Walter Kerr in the Channel Squadron, and was confirmed as a sub-lieutenant on 29 May 1900. In early December 1901 he was posted to the cruiser , but the order was cancelled as he was instead ordered to the cruiser as she left to become flagship of the Pacific Station in January 1902. He was promoted to lieutenant on 29 May 1902, and later the same year was posted to the cruiser as she was commissioned for the Pacific Station.