To detect ultra-high-energy neutrinos, experiments such as ARA and RNO-G target the radio emission induced by these particles as they cascade in the ice, using deep in-ice antennas at the South Pole or in Greenland. In this context, it is essential to first characterize the in-ice radio signature from cosmic-ray-induced particle showers, which constitute a primary background for neutrino detection, and represent the fist in-situ detection of in-ice particle cascades with radio antennas. This characterization will help validate the detection principle and assist in calibration. To achieve this goal, we used FAERIE, the ``Framework for the simulation of Air shower Emission of Radio for in-Ice Experiments'', that combines CoREAS and GEANT4 to simulate the radio emission of cosmic ray showers deep in the ice. Using this tool, we analyze in-ice radio signatures of cosmic-ray showers, including polarization, timing, and radiation energy, as well as their dependence on shower parameters. These insights will facilitate the first cosmic-ray detections and improve cosmic-ray/neutrino discrimination.