In this paper, we initiate the study of rate-splitting multiple access (RSMA) for a mono-static integrated sensing and communication (ISAC) system, where the dual-functional base station (BS) simultaneously communicates with multiple users and detects multiple moving targets. We aim at optimizing the ISAC waveform to jointly maximize the max-min fairness (MMF) rate of the communication users and minimize the largest eigenvalue of the Cramér-Rao bound (CRB) matrix for unbiased estimation. The CRB matrix considered in this work is general as it involves the estimation of angular direction, complex reflection coefficient, and Doppler frequency for multiple moving targets. Simulation results demonstrate that RSMA maintains a larger communication and sensing trade-off than conventional space-division multiple access (SDMA) and it is capable of detecting multiple targets with a high detection accuracy. The finding highlights the potential of RSMA as an effective and powerful strategy for interference management in the general multi-user multi-target ISAC systems.