In this paper, we investigate resource allocation algorithm design for intelligent reflecting surface (IRS)-assisted multiuser cognitive radio (CR) systems. In particular, an IRS is deployed to mitigate the interference caused by the secondary network to the primary users. The beamforming vectors at the base station (BS) and the phase shift matrix at the IRS are jointly optimized for maximization of the sum rate of the secondary system. The algorithm design is formulated as a non-convex optimization problem taking into account the maximum interference tolerance of the primary users. To tackle the resulting non-convex optimization problem, we propose an alternating optimization-based suboptimal algorithm exploiting semidefinite relaxation, the penalty method, and successive convex approximation. Our simulation results show that the system sum rate is dramatically improved by our proposed scheme compared to two baseline schemes. Moreover, our results also illustrate the benefits of deploying IRSs in CR networks.