He was educated at Westminster School and Christ Church, Oxford (BA 1730, MA 1733, BD & DD 1748).

In 1777 he was created Baron Rokeby, of Armagh in the County of Armagh, in the Peerage of Ireland,[1] with special remainder to Matthew Robinson (1694–1778) of West Layton, in the North Riding of the county of Yorkshire, his second cousin, twice removed, who predeceased him.

Archbishop Lord Rokeby died at Clifton in Bristol on 10 October 1794, and was buried in Armagh Cathedral.

Richard Cumberland described him as "splendid, liberal, lofty ... publicly ambitious of great deeds, and privately capable of good ones, ... he made no court to popularity by his manners but he benefited a whole nation by his public works".

[4] The Canterbury Gate at Christ Church, Oxford, completed in 1873, is one monument to Archbishop Lord Rokeby's munificence.