In this paper, a novel scheme based on polar codes is presented to deal with the high peak-to-average power ratio (PAPR) problem in the orthogonal frequency division multiplexing (OFDM) system. The proposed method uses the frozen bits in polar codes to generate an offset. Then, the offset is added to the encoded codeword such that the transmitted codeword can have a lower PAPR. Also, an algorithm is proposed to find the appropriate combination of frozen bits for a given dimension and a codeword length. In some cases, the transmitted codeword lies in a certain Golay complementary set (GCS). Therefore, the transmitted codeword has upper-bounded PAPRs due to the well-known PAPR property of the GCS. In comparison with the selected mapping (SLM) scheme, the proposed scheme has lower computational complexity since the values of the frozen bits are determined in advance. Simulation results show that the proposed algorithm offers good PAPR reduction without affecting the decoding performance of the polar code.