Alexander Abercromby was the youngest son of Sir Ralph Abercromby, a British lieutenant-general noted for his services during the Napoleonic Wars and Mary Abercromby, 1st Baroness Abercromby. Born on 4 March 1784, Abercromby entered the army at an early age, and served as a volunteer with the 92nd Regiment in the expedition to the Helder in 1799. He soon obtained a commission, and saw service with his regiment in Egypt. He was appointed aide-de-camp to his father's old lieutenant and friend, Sir John Moore, during his command in Sicily in 1806, but was not with him in Spain.