The elder son of the Reverend E. Rolfe, he was born at Cranworth, Norfolk, and educated at Bury St Edmunds, Winchester, and Trinity College, Cambridge. He was called to the bar at Lincoln's Inn in 1816, and attached himself to the chancery courts. He represented Penryn and Falmouth in parliament from 1832 till his promotion to the bench as baron of the exchequer in 1839. In 1850 he was appointed a vice-chancellor and created Baron Cranworth, and in 1852 he became Lord Chancellor in Aberdeen's ministry. He continued to hold the chancellorship under Lord Palmerston until the latter's resignation in 1857. He was not reappointed when Palmerston returned to office in 1859, but on the retirement of Lord Westbury in 1865 he accepted the great seal for a second time, and held it till the fall of the Russell administration in 1866.
Never a very zealous law reformer, Cranworth's name is associated in the statute book with only one small measure on conveyancing. But as a judge he will continue to hold first rank. His judgments were marked by sound common sense, while he himself was remarkably free from the prejudices of his profession. Few men of his day enjoyed greater personal popularity than Cranworth. He left no issue and the title became extinct on his death.