According to Murray's Clerk of Superior Court's office, Rhodes pled guilty to count three and Judge William Boyett ordered a pre-sentence investigation.
The small-town mayor was arrested by Federal Bureau of Investigations agents in October when he believed he was going to meet a minor he had met online for sexual purposes.
Rhodes was arrested on charges of aggravated child molestation and violation of the Computer Pornography and Child Exploitation Act. There is no allegation, however, that Rhodes possessed any wrongful images of children, according to Rhodes' attorney, Donald Evans.
Evans said on Thursday that counts one and two of the indictment charging Rhodes with attempted child molestation were dismissed.
"The Rhodes family has been through a lot, and [Cary] is trying to move on with his life," Evans said. "He is still the mayor and has had a lot of community support."
Rhodes is scheduled to be sentenced June 27 at 9 a.m.