In this paper, a novel Radar and wireless communication fusion system, namely RadCom, using orthogonal frequency division multiplexing index modulation (OFDM-IM) waveforms is studied. From the communication perspective, information is conveyed not only through modulated OFDM subcarriers but also by the active subcarrier indices that are dynamically updated at the transmitted symbol rates. When compared with conventional OFDM communication systems, only a subset of subcarriers is activated in the proposed OFDM-IM system, which reduces signal peak-to-average-ratios(PAPRs), leading to enhanced power amplifier (PA) efficiency. From the Radar sensing perspective, the Radar range-velocity profile obtained using compressed sensing (CS) approach is simulated and presented. It is shown that OFDM-IM RadCom system can enhance the transmission data rates when low-order modulation schemes are adopted, e.g. binary phase shift keying (BPSK), and maintain similar Radar performance compared with the OFDM counterpart when the system is carefully designed.