Reconfigurable intelligent surface (RIS) based reflection modulation has been considered as a promising information delivery mechanism, and has the potential to realize passive information transfer of a RIS without consuming any additional radio frequency chain and time/frequency/energy resources. The existing on-off reflection modulation (ORM) schemes are based on manipulating the "on/off" states of RIS elements, which may lead to the degradation of RIS reflection efficiency. This paper proposes a frequency reflection modulation (FRM) method for RIS-aided OFDM systems. The FRM-OFDM scheme modulates the frequency of the incident electromagnetic waves, and the RIS information is embedded in the frequency-hoping states of RIS elements. Unlike the ORM-OFDM scheme, the FRM-OFDM scheme can achieve higher reflection efficiency, since the latter does not turn off any reflection element in reflection modulation. We propose a block coordinate descent (BCD) algorithm to maximize the user achievable rate for the FRM-OFDM system by jointly optimizing the phase shift of the RIS and the power allocation at the transmitter. Further, we design a bilinear message passing (BMP) algorithm for the bilinear recovery of both the user symbols and the RIS data. Numerical simulations have verified the efficiency of the designed BCD algorithm for system optimization and the BMP algorithm for signal detection, as well as the superiority of the proposed FRM-OFDM scheme over the ORM-OFDM scheme.