The video was taken when the group took over part of a highway Sunday night, chanting and surrounding police vehicles.
The police chief is defending the officers, saying they were trying to reroute the protesters when the group began attacking the car.
The officers thought they were being shot at when the back window was smashed.
It was not known whether any of the protesters were seriously injured.
The incident is under investigation.
VIDEO: Woman plows car through crowd of protesters in West Hollywood
Woman plows car through crowd of protesters in West Hollywood: VIDEO