Yes! In a December 2020 update, Zoom extended the ability to launch and manage breakout rooms to co-hosts, which is the role that is typically assigned to a TA. This includes assigning students to breakout rooms.
Before this update, co-hosts had very limited access to breakout rooms in Zoom. The only thing they could do was freely move between breakout rooms once the host (i.e., the instructor) launched them.
Visit Zoom’s Help Center to view a list of all of the permissions for reach of its roles.