In this letter, we study a rate-splitting multiple access (RSMA)-based intelligent reflecting surface (IRS)-aided multi-user multiple-input single-output (MISO) secure communication system with a potential eavesdropper (Eve). Aiming to maximize the minimum secrecy rate (SR) among all the legitimate users (LUs), a design problem for jointly optimizing the transmit beamforming with artificial noise (AN), the IRS beamforming, and the secrecy common rate allocation is formulated. Since the design problem is highly non-convex with coupled optimization variables, we develop a computationally efficient algorithm based on the alternating optimization (AO) technique to solve it suboptimally. Numerical results demonstrate that the proposed design can significantly improve the max-min SR over the benchmark schemes without IRS or adopting other multiple access techniques. In particular, employing the RSMA strategy can substantially reduce the required numbers of IRS elements for achieving a target level of secrecy performance compared with the benchmark schemes.