Michael Cullen, 39, also allegedly provided a false statement and documentation to officers between May and April 2018.
Cullen, who now independently represents Glasgow’s Garscadden and Scotstounhill ward, is said to have made the false claim in March 2017.
Prosecutors allege he “falsely represented” to three police officers that he had been sexually assaulted in October 2014.
The charge states Cullen claimed he had been the “victim of sexual assault” and caused officers to devote time and services at the public expense to an investigation.
It further claims Cullen knew the claim was false.
Cullen faces a second charge of attempting to pervert the course of justice.
He is said to have claimed that he was impacted mentally and financially by the alleged sexual assault in a review application.