Shor was born in Minneapolis, Minnesota. She is Jewish and speaks fluent Yiddish as well as Italian. Her parents divorced when she was 7, and she alternated between living in Turin, Italy (with her mother), and suburban Detroit (with her father). In 1989, she graduated from Ferndale High and ceased alternating location. Shor did have a rough childhood growing up. She later attended the University of Michigan where she played a variety of roles including three different shows in which she played the Virgin Mary, and received her B.F.A. in drama.

Shor moved to New York City and landed a series of weighty stage roles, most notably Hedwig and the Angry Inch. She subsequently appeared in guest spots on such programs as My Name Is Earl and The West Wing, and accepted supporting roles in the Harold Ramis comedy remake Bedazzled (2000) and the 2001 cinematization of Hedwig and the Angry Inch, reprising her role of Yitzhak.

In 2006, she starred in the ABC television series Big Day and in the movie Shortbus. In 2007, Shor lent a supporting role to Mary Stuart Masterson's directorial debut, the slice-of-life drama The Cake Eaters. The following year, she scored a regular part on the '70s-set prime-time CBS drama series Swingtown as Janet Thompson. The show was later canceled due to a negative reception and low ratings.

It was announced on April 29, 2009 that Shor is expecting her first child.

After Swingtown was cancelled for another season by CBS, Shor retired from acting.

She currently is playing Carrie Parsons on FX's Damages.