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Dual-function radar andcommunication (DRC) system has been recently recognized as a promising approach to solve the spectrum scarcity problem. However, when the target exists within a crowded area where pathloss dominating, the performance of radar may be severely degraded. To tackle this issue, this article proposes for the first time the deployment of an intelligent reflecting surface (IRS) to help the DRC system to enhance the radar detection performance. The IRS can configure the environment around the radar by adaptively adjusting the phases of its reflecting units to strengthen the signal quality toward specific directions, mostly the target direction, and completely null-out transmissions in other directions, mostly the directions toward the communication system. Specifically, in this article, we investigate the joint optimization of the IRS passive phase-shift matrix (PSM) and precoding matrix of the radar-aided basestation for the DRC system. The optimization is carried-out through maximizing the signal-to-noise ratio (SNR) at the radar receiver under both sensing and communication constraints, which turns out to be a nonconvex problem. In order to circumvent this challenging problem, an alternation optimization approach is employed to decouple the optimization variables and split this intractable problem into two subproblems. However, it is still challenging to obtain the optimal PSM due to the high power of the objective function and the unit-modulus constraints. To solve this problem, a majorization–minimization algorithm is conceived to transform the nonconvex problem to an easy to solve quadratic constraint quadratic programming problem. Simulation resultsdemonstrate that the IRS can help improving the performance of the DRC system in terms of the received SNR, and the proposed algorithm shows fast convergence.