His son, George B. Rodney Jr., served as governor of Alaska for four months in 1874.

Rodney served as Register in Chancery and Clerk of the Orphans’ Court of Sussex County from 1826 until 1830.

He was elected as a Whig and served four years representing Delaware in the U.S. House of Representatives in the 27th and 28th congresses, from March 4, 1841, until March 3, 1845, during the administrations of U.S. presidents William Henry Harrison and John Tyler.

Following his retirement he resumed the practice of law and served as a delegate to the peace convention held in Washington, D.C., in 1861 in an effort to prevent the impending Civil War.

Rodney died at New Castle and is buried there in the Immanuel Episcopal Church Cemetery.