Intelligent reflecting surface (IRS) has been proved to be an efficient technology to improve the spectrum and energy efficiency in cognitive radio (CR) networks. Unfortunately, due to the fact that the primary users (PUs) and the secondary users (SUs) are non-cooperative, it is challenging to obtain the perfect PUs-related channel sate information (CSI). In this paper, we investigate the robust beamforming design based on the statistical CSI error model for PU-related cascaded channels in IRS-aided CR systems. We jointly optimize the transmit precoding (TPC) matrix and phase shifts to minimize the SU's total transmit power, meanwhile subject to the quality of service (QoS) of SUs, the interference imposed on the PU and unit-modulus of the reflective beamforming. The non-convex optimization problems are transformed into two second-order cone programming (SOCP) subproblems and efficient algorithms are proposed for solving these subproblems. Simulation results verify the efficiency of the proposed algorithms and reveal the impacts of CSI uncertainties on ST's transmit power and feasibility rate of the optimization problem.