After he was State Representative, Carney was elected Governor of Kansas. He was governor from 1863 through 1865. While he was governor, he focused on developing the state and solving the problems caused by the Civil War. He was elected Mayor of Leavenworth in 1865. He created the First National Bank of Leavenworth. He was also director of the Lawrence and Fort Gibson Railroad Company. He continued in business until 1875.