arcovicci was born in New York City, the daughter of Helen (née Stuart), a singer, and Eugene Marcovicci, a physician and internist. In her teens, she decided that she wanted to be a singer, but instead majored in drama. In a 1972 interview, she looked back at this period without enthusiasm:
"I found that people interested in theater were very serious and heavy. It was a very inbred group. I could not be a part of that.