In this letter, we investigate the robust beamforming design for an integrated sensing and communication (ISAC) system featuring low-resolution digital-to-analog converters (DACs) and analog-to-digital converters (ADCs). Taking into account quantization noise, we aim at maximizing the radar signal-to-quantization-plus-noise ratio (SQNR) while guaranteeing the minimum required signal-to-quantization-plus-interference-plus-noise ratio (SQINR) for communication users. To address this nonconvex design problem, we first examine a scenario involving a point target and uniform-resolution DACs, where the globally optimal solution is obtained by applying the semidefinite relaxation (SDR) technique. For more general scenarios, including those with mixed-DACs and/or an extended target, we develop a low-complexity majorization-minimization (MM)-based algorithm to tackle the problem iteratively. Compared to the non-robust algorithm, the proposed algorithm demonstrates improved detection performance under practical quantization. Simulation results confirm the robustness and efficacy of our proposed algorithm in low-resolution quantization scenarios.