Fault zone structures at many scales largely dictate earthquake ruptures and are controlled by the geologic setting and slip history. Characterizations of these structures at diverse scales inform better understandings of earthquake hazards and earthquake phenomenology. However, characterizing fault zones at sub-kilometer scales has historically been challenging, and these challenges are exacerbated in urban areas, where locating and characterizing faults is critical for hazard assessment. We present a new procedure for characterizing fault zones at sub-kilometer scales using distributed acoustic sensing (DAS). This technique involves the backprojection of the DAS-measured scattered wavefield generated by natural earthquakes. This framework provides a measure of the strength of scattering along a DAS array and thus constrains the positions and properties of local scatterers. The high spatial sampling of DAS arrays makes possible the resolution of these scatterers at the scale of tens of meters over distances of kilometers. We test this methodology using a DAS array in Ridgecrest, CA which recorded much of the 2019 Mw7.1 Ridgecrest earthquake aftershock sequence. We show that peaks in scattering along the DAS array are spatially correlated with mapped faults in the region and that the strength of scattering is frequency-dependent. We present a model of these scatterers as shallow, low-velocity zones that is consistent with how we may expect faults to perturb the local velocity structure. We show that the fault zone geometry can be constrained by comparing our observations with synthetic tests.