Weinstein, 67, has pleaded not guilty to sexually assaulting two other women, Mimi Haleyi and Jessica Mann.
While Sciorra's allegation is too old to support a separate rape charge against Weinstein, prosecutors hope it will show that he is a repeat sexual predator - a charge that could put him in prison for life.
Since 2017, more than 80 women, including many famous actresses, have accused Weinstein of sexual misconduct.
The accusations fueled the #MeToo movement, in which women have accused powerful men in business, entertainment, media and politics of sexual misconduct.
Weinstein, who reshaped the independent film industry with critically acclaimed pictures such as “The English Patient” and “Shakespeare in Love,” has denied the allegations and said any sexual encounters were consensual.
The trial is widely seen as a watershed moment for the movement.
Prosecutors in opening statements on Wednesday portrayed Weinstein as a serial predator whose victims experienced shame and humiliation following encounters with him.
Weinstein's lawyers have said that messages from his accusers would show they maintained warm relations with him after the alleged attacks.. The defense maintains the women reframed consensual encounters as nonconsensual after the fact.
Sciorra, who appeared in "The Sopranos," testified on Thursday that Weinstein gave her a ride home with his driver after a dinner one winter night in 1993 or 1994. She said that after dropping her off, he knocked on her door unannounced, forced his way in and raped her.Actress Rosie Perez, a longtime friend of Sciorra, testified on Friday that Sciorra told her about the rape soon after it happened. She said she urged Sciorra to go to the police, but Sciorra refused, saying, "He'd destroy me."