This paper considers reconfigurable intelligent surface (RIS)-aided integrated sensing and communication (ISAC) systems under dual-polarized (DP) channels. Unlike the existing ISAC systems, which ignored polarization of electromagnetic waves, this study adopts DP base station (BS) and DP RIS to serve users with a pair of DP antennas. The achievable sum rate is maximized through jointly optimizing the beamforming matrix at the DP BS, and the reflecting coefficients at the DP RIS. To address this problem, we first utilize the weighted minimum mean-square error (WMMSE) method to transform the objective function into a more tractable form, and then an alternating optimization (AO) method is employed to decouple the original problem into two subproblems. Due to the constant modulus constraint, the DP RIS reflection matrix optimization problem is addressed by the majorization-minimization (MM) method. For the DP beamforming matrix, we propose a penalty-based algorithm that can obtain a low-complexity closed-form solution. Simulation results validate the advantage of deploying DP transmit array and DP RIS in the considered ISAC systems.