The Murchison Widefield Array (MWA) is a new low-frequency interferometric radio telescope, operating in the benign radio frequency environment of remote Western Australia. The MWA is the low-frequency precursor to the Square Kilometre Array (SKA) and is the first of three SKA precursors to be operational, supporting a varied science mission ranging from the attempted detection of the Epoch of Reionization to the monitoring of solar flares and space weather. In this paper we explore the possibility that the MWA can be used for the purposes of Space Situational Awareness (SSA). In particular we propose that the MWA can be used as an element of a passive radar facility operating in the frequency range 87.5-108 MHz (the commercial FM broadcast band). In this scenario the MWA can be considered the receiving element in a bi-static radar configuration, with FM broadcast stations serving as non-cooperative transmitters. The FM broadcasts propagate into space, are reflected off debris in Earth orbit, and are received at the MWA. The imaging capabilities of the MWA can be used to simultaneously detect multiple pieces of space debris, image their positions on the sky as a function of time, and provide tracking data that can be used to determine orbital parameters. Such a capability would be a valuable addition to Australian and global SSA assets, in terms of southern and eastern hemispheric coverage. We provide a feasibility assessment of this proposal, based on simple calculations and electromagnetic simulations, that shows that the detection of sub-meter size debris should be possible (debris radius of >0.5 m to 1000 km altitude). We also present a proof-of-concept set of observations that demonstrate the feasibility of the proposal, based on the detection and tracking of the International Space Station via reflected FM broadcast signals originating in southwest Western Australia.