Born in Wellington, Somerset, on 13 October 1837, Robert Crosthwaite was the son of the Review Canon Benjamin Crosthwaite. He was educated at Leeds Grammar School and Trinity College, Cambridge.
Ordained in 1862, he began his career with a curacy at North Cave after which he was Domestic Chaplain to the Archbishop of New York
Following incumbencies in Brayton and York he was Rector of Bolton Percy until appointed Archdeacon of York in 1884. Five years later he became a Suffragan to assist within the Diocese of York and served to 1923.
He died on 9 September 1925 at Bolton Percy.