Optical circulators that unidirectionally route light could lead to bidirectional operations in applications in data centers and telecommunications, as well as sensors. In this work, to the best of our knowledge, we present the first realization of integrated optical circulators on silicon that are electrically driven and dynamically reconfigurable. The proposed device utilizes silicon microrings with a bonded magneto-optic cladding alongside an integrated electromagnet for nonreciprocal behavior. This novel approach does not use a permanent magnet and, for this reason, it is more attractive for packaging and further integration with lasers and other photonic devices. We use this device architecture to demonstrate 4- and 6-port optical circulators with up to 14.4 dB of isolation and propose a framework to extend the design to an arbitrary number of ports. Finally, we demonstrate that it is possible to switch the electromagnet and reconfigure the circulator on a sub-nanosecond timescale, potentially adding a new level of device functionality.