Vicars was born on 27 July 1862 in Leamington Spa, Warwickshire, and was the youngest child of Colonel William Henry Vicars of the 61st Regiment of Foot and his wife Jane (originally Gun-Cunninghame). This was his mother's second marriage, the first being to Pierce O'Mahony by whom she had two sons. Arthur was very attached to his Irish half-brothers and spent much time at their residences. On completing his education at Magdalen College School, Oxford and Bromsgrove School he moved permanently to Ireland.