In the recording released by TMZ Sports, the 19-year-old woman said, "I was assaulted and I need help."
When asked who assaulted her, she responded, "I think his first name is Kareem."
Hunt denied the allegations and no arrests were made when police arrived on the scene because they could not determine if someone had been assaulted.
While the woman said Hunt shoved her, TMZ Sports reported in February that Hunt's friends provided a different account.
They said the woman was asked to leave the party when it was discovered that she was only 19, which allegedly led to her punching one of Hunt's female friends in the face and directing a racial slur at Hunt.
On June 6, TMZ reported a man said had that Hunt punched him in the face at a resort in Put-in-Bay, Ohio. The alleged victim does not intend to press charges.
The 22-year-old Hunt burst onto the scene last season. He led the NFL with 1,327 rushing yards as a rookie, finished second in Offensive Rookie of the Year voting and was named to the Pro Bowl.