Judge David Bramlette sentenced Sims in U.S. District Court in Jackson on Tuesday. Sims also will serve six months under house arrest.
Sims was charged in October 2011 with sexually assaulting the prisoner while acting in his official capacity and intimidating a witness. He pleaded guilty to the intimidation charge in February and was forced to resign as mayor.
Sims was first elected mayor in 1981. He became warden of the Walnut Grove Transition Center in October 2009. Prosecutors say he had sex with the inmate in a Carthage hotel in November 2009.