We present a particle-level model for calculating the radio scatter of incident RF radiation from the plasma formed in the wake of a particle shower. We incorporate this model into a software module ("RadioScatter"), which calculates the collective scattered signal using the individual particle equations of motion, accounting for plasma effects, transmitter and receiver geometries, refraction at boundaries, and antenna gain patterns. We find appreciable collective scattering amplitudes with coherent phase for a range of geometries, with high geometric and volumetric acceptance. Details of the calculation are discussed, as well as the implementation of RadioScatter into GEANT4. A laboratory test of our model, currently scheduled at SLAC in 2018, with the goal of measuring the time-dependent characteristics of the reflecting plasma, is also described. Prospects for a future in-ice, high-energy neutrino detector, along with comparison to current detection strategies, are presented.