Cosby’s lawyer Jennifer Bonjean told US media her client would appeal against Monday’s verdict.
The jury in the Santa Monica case could award even more in punitive damages that they have yet to determine.
Motsinger, now 84, used to work as a waitress at a restaurant called the Trident in Sausalito, near San Francisco, that was a haunt for celebrities, including Cosby.
She alleged in her lawsuit that Cosby invited her to one of his stand-up comedy shows and after picking her up to drive her to the gig he gave her a pill that she thought was aspirin, according to the court papers.
“Next thing she knew, she was going in and out of consciousness,” her legal action said, according to the Los Angeles Times. “The last thing Ms Motsinger recalls were flashes of light.”
The filing said she woke up at home naked except for her underwear and “she knew she had been drugged and raped by Bill Cosby”.
Cosby’s lawyers rejected the allegation, arguing in court filings that Motsinger “freely admits that she has no idea what happened”, reports AP news agency.
His spokesperson and lawyer did not respond to the BBC’s requests for comment.
The comedian enjoyed huge fame in the 1980s and 90s with his sitcom The Cosby Show, but his reputation was shattered after dozens of women came forward with allegations of rape, sexual harassment and sexual misconduct from as early as the 1960s. He has maintained all of the encounters were consensual.