Robert Cox Clifton (1810–1861) was an English churchman, canon of Manchester Cathedral.
Clifton was the son of a clergyman, for many years British chaplain at Bruges, and was born at Gloucester on 4 January 1810.
Before taking his first curacy, which was in Berkshire, he spent some time in Oxford as a tutor.
In 1843 he was instituted to the rectory of Somerton in Oxfordshire, a benefice he held with his Manchester preferment until his death.
He took part in the administration of public charities and religious societies in Manchester, and was a trustee of Owens College, where his son Robert Bellamy Clifton was for some time professor of experimental philosophy.