This work is the first to introduce the rate splitting multiple access (RSMA) scheme for cognitive radio (CR) networks. The particle swarm optimization (PSO) is applied to get the best beamforming vectors and common rate vectors that achieve the maximum energy efficiency (EE). It is assumed that arbitrary numbers of primary users (PUs) and secondary users (SUs) exist in the system. The proposed system design is based on the application of the optimization process as described above while maintaining the constraint that the signal-to-interference-plus-noise ratio (SINR) for any PU shall be greater than a specified minimum value. In this way, not only the SINR at any PU is maintained higher than a pre-set minimum value to ensure higher priority than any other SU but also the fairness between the PUs themselves is realized to a satisfactory level. The effects of the operational parameters in CR networks such as the number of PUs and SUs, the number of transmitting antennas, the efficiency of the power amplifier, and the dynamic power consumed by a transmitting antenna are numerically investigated.