Movable antennas (MAs) have shown significant potential in enhancing the performance of dual-functional radar-communication (DFRC) systems. In this paper, we investigate the MA-based transceiver design for DFRC systems, where a reconfigurable intelligent surface (RIS) is employed to enhance the communication quality in dead zones. To enhance the radar sensing performance, we formulate an optimization problem to maximize the radar signal-to-interference-plus-noise ratio (SINR) by jointly optimizing the beamforming vectors, receiving filter, antenna positions, and RIS reflecting coefficients. To tackle this challenging problem, we develop a fractional programming-based optimization framework, incorporating block coordinate descent (BCD), successive convex approximation (SCA), and penalty techniques. Simulation results demonstrate that the proposed method can significantly improve the radar SINR and achieve a satisfactory balance between the radar and communication performance compared with existing benchmark schemes.