Hinkson was elected to the Ohio House of Representatives in 1826, 1827 1829, 1830 and 1833.[2] During the 1833-1834 session, the legislature elected him as Secretary of State. He served until he resigned February 12, 1836.[3]
In 1836, Hinkson was elected president judge of the Court of Common Pleas for the district of Clinton, Warren, Butler, and Greene counties. He served a term of seven years, and returned to private practice.[1]
In 1852, Hinkson retired from law practice and engaged in stock raising on his farm. He died of paralysis in his 78th year in March, 1877.[1]