The girl claims the she began to communicate on Facebook with Henry Hopper who then invited her to his home in Venice, California, on several occasions with the promise of drugs and alcohol, TMZ reported.
The girl's mother, who has launched the civil action, claims Hopper, who starred in "Restless" in 2011, would wait until her daughter was intoxicated before he "engaged in sexually offensive conduct with her".
TMZ said it was unclear if the girl ever reported the allegations to police.
New York Daily News said the law suit claims the actor "preyed upon a young impressionable child, suggesting that he cared for her, luring her into his home with promises of alcohol and illegal drugs, and then repeatedly taking advantage of her youth an vulnerability."
It is alleged the girl, referred to as Jan Doe, suffered significant injuries to her emotional health, strength and activity, and required psychological treatment.
She's suing for unspecified damages. Attempts by media outlets to reach Hopper were unsuccessful.