Thomas Rundle (c.1688–1743) was an English cleric suspected of unorthodox views. He became Anglican bishop of Derry not long after a high-profile controversy had prevented his becoming bishop of Gloucester in 1733.
He was born at Milton Abbot, Devon, about 1688, son of Thomas Rundle, an Exeter clergyman. After Exeter grammar school under John Reynolds, he matriculated as a commoner at Exeter College, Oxford, on 5 April 1704, at the age of 16. He took the degree of B.C.L. in 1710.
In 1712 Rundle made the acquaintance of William Whiston, in Oxford for patristic study and to find support for his Society for Promoting Primitive Christianity. Rundle and his tutor Thomas Rennel were sympathetic, but thought Whiston would find no other local recruits. Rundle in the same year became tutor to the only son of John Cater of Kempston, near Bedford. Here Whiston visited him, and suggested a critical examination of the Sibylline oracles, which he didn't complete. Going to London, he attended of Whiston's society, which held meetings from 3 July 1715 to 28 June 1717; but Thomas Emlyn found Rundle worldly. Rundle informed Whiston that he intended to take holy orders, which Whiston took badly; and became more a follower of Samuel Clarke.
Rundle was ordained deacon on 29 July, and priest on 5 August 1716, by William Talbot as bishop of Salisbury; his younger son Edward had been Rundle's close friend since Oxford days. Talbot made Rundle his domestic chaplain, and gave him a prebend of Salisbury Cathedral. Rundle became vicar of Inglesham, Wiltshire, in 1719, and rector of Poulshot, Wiltshire, in 1720, both livings being in the bishop's gift. Talbot appointed him archdeacon of Wilts (1720), and treasurer of Sarum (1721).