In this letter, we investigate the secrecy rate of an reconfigurable intelligent surface (RIS)-aided millimeter-wave (mmWave) system with hardware limitations. Compared to the RIS-aided systems in most existing works, we consider the case of the RIS-aided mmWave system with low-resolution digital-to-analog converters (LDACs). We formulate a secrecy rate maximization problem hardware constraints. Then by optimizing the RIS phase shift and the transmit beamforming to maximize the secrecy rate. Due to the nonconvexity of the problem, the formulated problem is intractable. To handle the problem, an alternating optimization (AO)-based algorithm is proposed. Specifically, we first use the successive convex approximation (SCA) method to obtain the transmit beamforming. Then the element-wise block coordinate descent (BCD) method is used to obtain the RIS phase shift. Numerical results demonstrate that the RIS can mitigate the hardware loss, and the proposed AO-based algorithm with low complexity outperformances the baselines.