Movable antennas (MAs) fully exploit spatial degrees of freedom (DoFs) in continuous space through dynamic position adjustment, thereby enhancing the performance of integrated sensing and communication (ISAC) systems. This paper investigates robust beamforming and antenna position optimization in MA assisted ISAC systems under bounded channel uncertainty. A position-dependent channel estimation error model is first derived, jointly accounting for errors induced by antenna movement, angle estimation, and signal strength estimation. Based on this model, a robust optimization problem is formulated to maximize sensing performance while satisfying the signal-to-interference-plus-noise ratio (SINR) requirements of multiple communication users. To address the non-convexity arising from the coupling between antenna positions and beamforming vectors, a low-complexity alternating optimization algorithm is developed, incorporating the S-procedure, semidefinite relaxation (SDR), and successive convex approximation (SCA). Simulation results demonstrate that the proposed algorithm significantly outperforms fixed-position antenna (FPA)-based schemes, achieving up to a 40% improvement in sensing beampattern gain while ensuring the SINR requirements.