Younger brother of Martin Rodda, born at Sancreed, Cornwall and baptized on 29 May 1743. He joined the Methodist society in 1756 and was converted in 1758. He worked as a tin miner and had several providential escapes from death. He was conscripted into the navy in 1759, but released through the intervention of a Quaker. He became a local preacher and accompanied his itinerant brother to Wales at least twice between 1765 and 1768. He entered the ministry in 1769 and was sent by John Wesley to Glamorgan. He became a frequent correspondent with Wesley. He was one of the preachers named in the Deed of Declaration as one of the 'Legal Hundred' and became a leading figure in the years after John Wesley's death. He was one of those involved in issuing the 'Halifax circular' and sided with the Church Methodists, or 'Old Planners', in opposing Samuel Bradburn and the administration of the Sacrament in Bristol in 1794. Suffering from asthma, brought on by the hardships of the itinerancy, he superannuated to Burslem for a year in 1797, and then finally in London in 1802. He died there on 30 October 1815 and was buried in Wesley's vault at City Road chapel.
John Pawson reported that Rodda's first wife, whom he had married in 1768, was drowned with two of their children sailing from Bristol to Pembroke in 1794. In December 1794 he married Elizabeth (1754-1835), a 'high church woman with £1,500' , on which Pawson adds the cryptic comment, 'so perhaps he may be quiet.'