Carissa Capeloto, who is now 22, is suing the three men for a total of $5 million, alleging she was "obviously intoxicated, incapable of consent" when she was assaulted after going to Kingston's hotel room for a meet-and-greet with the hip-hop artist after a 2010 concert, TMZ said.
Kingston, 23, replied to the lawsuit and said the sex was consensual.
TMZ said police were called following the incident and Capeloto was taken to a hospital where she said she was treated for physical injuries consistent with rape.
No criminal charges were filed against the men becaise there wasn't enough evidence a crime had taken place, the celebrity news website said.
A trial on the lawsuit is to begin in November.
Celebrity Families of 2014 [PHOTOS]
S Club 7 to reunite for BBC charity event