He was ordained in 1793 and became rector of Hunmanby in the East Riding. In England at that time, it was common for well-connected or conspicuously talented clerics to accumulate church positions, hiring curates to do the actual work. Wrangham's success resulted from his own talent and from an early position as tutor to the brother of the Duke of Manchester, and the lifelong friendship and patronage of the ducal family. In addition to being vicar of Humanby, Wrangham was vicar of Folkton, 1795–1821; Fellow of the Royal Society, 15 November 1804; examining chaplain to Vernon Harcourt, Archbishop of York, 1814–34; Archdeacon of Cleveland, 1820–28; vicar of Thorpe Bassett, 1821–27; Prebendary of York, 1823; rector of Dodleston, Cheshire, and Prebendary of Chester, 1827–42; and Archdeacon of the East Riding, 1828–41.