Henry Hopper -- who starred in Gus Van Zant's "Restless" in 2011 -- is being sued by the mother of an unidentified 16-year-old girl ... who claims the girl met Hopper through a mutual friend in Feb. 2011.

According to the legal papers, the girl -- identified in the lawsuit as Jan Doe -- claims the two began to communicate on Facebook ... and in the months that followed, Hopper invited her to his home in Venice, CA on multiple occasions with the promise of drugs and alcohol.

In the suit, Doe claims Hopper would wait until she was intoxicated ... and "engaged in sexually offensive conduct with her" ... including sexual intercourse, forced oral copulation and sodomy.

It's unclear if Doe ever reported the allegations to police.

In the suit, Doe's lawyer 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."

Doe's mother claims the girl suffered significant injuries to her emotional health, strength and activity ... and was required to employ multiple mental health care professionals for treatment.