An integrated radar and communications system (IRCS) where a monostatic radar transceiver is employed for target classification while simultaneously used as a communications transmitter is considered. The radar combined propagation-target response (joint response of the radar propagation channel and target) and communications channel response are generally frequency selective but the corresponding frequency response functions are not exactly known. In particular, these frequency response functions are only known to lie in an uncertainty class. To ensure the IRCS simultaneously provides acceptable target classification performance and communications rate, a robust orthogonal frequency division multiplexing (OFDM) integrated radar and communications waveform (IRCW) design method is proposed. The approach finds a waveform that simultaneously provides a sufficiently large weighted sum of the communications data information rate (DIR) and the conditional mutual information (MI) between the observed signal and the radar target over the entire uncertainty class. First, the conditional MI and DIR based on the integrated OFDM radar and communications waveform are derived. Then, a robust OFDM IRCW optimization problem based on the minimax design philosophy is developed such that closed-form solution is derived. Finally, several numerical results are presented to demonstrate the effectiveness of the proposed method.