Soil moisture can vary spatially at the scale of agricultural fields (~10 -100 m), which is generally too fine to resolve using passive radiometric methods. Active radar provides an opportunity for finer resolution measurements; in particular, the interferometric synthetic aperture radar (InSAR) closure phase parameter is sensitive to changing soil moisture. We have developed a model showing that systematic non-zero closure phase can result from scattering from objects at different depths in a medium of time-varying dielectric, such as from changes in soil moisture. The model predicts that interference between surface and subsurface reflections are needed for closure phase to be non-zero. We find that, under certain circumstances, we can estimate soil moisture from closure phase using a data reduction approach that includes a cumulative sum of closure phase over time and removal of a trend. The correlation between cumulative closure phase and soil moisture suggests that the closure phase is related to the change in soil moisture. We examined a large test region in Oklahoma, where the detrended cumulative closure phase from Sentinel-1 data demonstrates some agreement with in situ soil moisture measurements. In other areas, the match is weaker, implying a terrain dependence for the quality of fit. Cumulative InSAR closure phase promises to provide a valuable new method to remotely estimate soil moisture.