Rodgers was convicted in 2010 in Monroe County. He was sentenced to 15 years for armed robbery and 15 years for burglary of a residence. The sentences are running concurrently.
Prosecutors say an elderly Amory couple was severely beaten during the 2008 incident.
The state Court of Appeals upheld Rodgers' conviction in April. The Supreme Court on Thursday denied Rodgers' motion to hear the case.