Harvey Weinstein, the suit claims, repeatedly acted "to entice or recruit or solicit young female actors with the promise of roles in upcoming TWC projects ... knowing that he would then use fraud, force or coercion to engage in sex acts with these actors."
The suit alleges a violation of the sex trafficking statute, which prohibits people from recruiting people to engage in a sex act through means of force, threats of force, fraud or coercion.
The statute of limitations for sex trafficking is 10 years.
Holly Baird, Harvey Weinstein's spokesman, said: "Mr Weinstein denies allegations of non-consensual sex."
"Mr Weinstein has further confirmed that there were never any acts of retaliation against any women for refusing his advances." Bob Weinstein's spokesman, contacted by the Telegraph, did not respond to requests for comment.
Harvey Weinstein is also facing a damages claim in a London court by a woman who accuses him of sexual assault. Personal injury lawyer Jill Greenfield said her client, who hasn't been identified, is seeking damages for "personal injury" plus expenses and "consequential loss" arising out of a series of sexual assaults by Weinstein.
Civil claims for rape and sexual assault are uncommon in Britain.
Greenfield's firm, Fieldfisher, said that this is the first such claim in Britain against Weinstein, who has been accused of sexual harassment and assault by dozens of women.
Papers for the claim have been filed at the High Court, but no date has been set for a hearing.