Assistant District Attorney Meghan Hast told jurors that Weinstein raped Sciorra, best known for her role in HBO's "The Sopranos," on a winter night in 1993 or 1994. After giving her a ride home and dropping her off, Hast said, Weinstein knocked on her door unannounced, forced his way inside and assaulted her.
Weinstein's lawyer denies her account of events.
Sciorra's allegation is too old to be charged as a separate crime, but prosecutors hope it will show that Weinstein was a repeat sexual predator, a charge that could put him in prison for life.
Prosecutors have accused the 67-year-old Hollywood mogul with assaulting two women, Mimi Haleyi and Jessica Mann.
Weinstein has pleaded not guilty and said any sexual encounters were consensual.
The trial is a watershed moment for the #MeToo movement, in which women have gone public with allegations against powerful men in business and politics.
Since 2017, more than 80 women, including many famous actresses, have accused Weinstein of sexual misconduct.