In cognitive radio (CR) communication systems, achieving high secondary user (SU) rate in the presence of strong cross-link interference with the primary user (PU) is challenging. In this letter, we exploit the emerging intelligent reflecting surface (IRS) technology to tackle this problem. Specifically, we investigate an IRS-assisted CR communication system where an IRS is deployed to assist in the spectrum sharing between a PU link and an SU link. We aim to maximize the achievable SU rate subject to a given signal-to-interference-plus-noise ratio target for the PU link, by jointly optimizing the SU transmit power and IRS reflect beamforming. Since the formulated problem is difficult to solve due to its non-convexity and coupled variables, we propose an efficient algorithm based on alternating optimization and successive convex approximation techniques to solve it sub-optimally, along with some heuristic designs for lower complexity. Simulation results show that IRS is able to significantly improve the SU rate, even for the scenarios deemed most challenging in conventional CR systems without using IRS.