He was born of an old Highland family in Aberdeen, Scotland. In October 1838 he was admitted to deacon's orders, and after his return from Italy he took charge of the episcopal congregation at Forres, and was ordained a presbyter in the autumn of 1841. In 1846 he was elected first bishop of the newly restored diocese of Argyll and the Isles, the duties of which position he discharged till his death. In 1851 he received the degree of D.C.L. from the University of Oxford.
Though hampered by poor health, he worked cheerfully, and his personal charm and Catholic sympathies gradually won him a prominent position. In theological discussion he was tolerant, and attached little importance to ecclesiastical authority and organization. His own theological position had close affinity with that of Thomas Erskine of Linlathen and Frederick Denison Maurice; but his opinions were independent. The trend of his teaching is only to be gathered from fragmentary publications--letters to the newspapers, pamphlets, special sermons, essays contributed to the series of Present Day Papers, of which he was the editor, and a volume of sermons entitled Revelation considered as Light.
Besides his strictly theological writings, Ewing was the author of the Cathedral or Abbey Church of Iona (1865), the first part of which contains drawings and descriptive letterpress of the ruins, and the second a history of the early Celtic church and the mission of St Columba. See Memoir of Alexander Ewing, D.C.L., by AJ Ross (1877).