He entered The Queen's College, Oxford, as batler, on 21 February 1745, partly maintained by his elder brother, the Rev.
On 30 October 1769 he was appointed by Trevor to the rectory of Houghton-le-Spring, which he continued to hold until his death; and from 1778 to 1783, when he resigned the benefice in favour of his nephew[1] Richard Wallis, he was vicar of Seaham.
Rotheram was struck by a stroke at Bamburgh Castle, when visiting Archdeacon John Sharp, and died there on 16 July 1789.
His remains were laid near the grave of his brother, in the chancel of Houghton church, and a marble tablet was erected to his memory.
From Codrington College he produced the larger volume: A Sketch of the One Great Argument, formed from the several concurring Evidences for the Truth of Christianity (1754 and 1763).