Randolph was born into an ecclesiastical family: his father was a priest, Leveson Cyril Randolph. Educated at Eton and Trinity College, Cambridge, he was ordained into the priesthood in 1890. His first post was a curacy in Margate, after which he was Vicar of All Saints’, Westbrook, then St Mark’s, North End, before his appointment to the episcopate. He became a Doctor of Divinity (DD).