Two anomalous events have been reported by the ANITA collaboration that are observationally consistent with air showers from a particle emerging from the Antarctic ice. One possible interpretation of these events is that they are due to tau neutrinos interacting in the Earth, resulting in an air shower initiated by a tau lepton decay. We present a comprehensive study of the sensitivity of ANITA to tau neutrinos, using the expected Standard Model cross-sections and tau lepton energy losses, varied ice thicknesses, and radio emission simulation of upgoing tau showers with ZHAireS.