The detection of high-energy neutrinos in the EeV range requires new detection techniques in order to cope with the small expected flux. The radio detection method, utilizing Askaryan emission, can be used to detect these neutrinos in polar ice. The propagation of the radio pulses has to be modeled carefully in order to reconstruct the energy, direction and flavor of the neutrino from the detected radio pulses. In this contribution, we study the effect of birefringence in ice, which provides useful signatures to determine the neutrino energy and is potentially important to determine the neutrino direction to degree precision. We developed a detailed model, which propagates full RF waveforms, implemented it into the NuRadioMC framework and applied it to the ice of the South Pole. Finally, we compare our results to in-situ calibration data from the ARA and ARIANNA experiments, and discuss the implications for neutrino detection.