In this paper, we present a new inter-carrier interference (ICI) self-cancellation scheme - namely, ISC scheme - for orthogonal frequency-division multiplexing systems to reduce the ICI generated from phase noise (PHN) and residual frequency offset (RFO). The proposed scheme comprises a new ICI cancellation mapping (ICM) scheme at the transmitter and an appropriate method of combining the received signals at the receiver. In the proposed scheme, the transmitted signal is transformed into a real signal through the new ICM using the real property of the transmitted signal; the fast-varying PHN and RFO are estimated and compensated. Therefore, the ICI caused by fast-varying PHN and RFO is significantly suppressed. We also derive the carrier-to-interference power ratio (CIR) of the proposed scheme by using the symmetric conjugate property of the ICI weighting function and then compare it with those of conventional schemes. Through simulation results, we show that the proposed ISC scheme has a higher CIR and better bit error rate performance than the conventional schemes.