Rate splitting multiple access (RSMA) is regarded as a crucial and powerful physical layer (PHY) paradigm for next-generation communication systems. Particularly, users employ successive interference cancellation (SIC) to decode part of the interference while treating the remainder as noise. However, conventional RSMA systems rely on fixed-position antenna arrays, limiting their ability to fully exploit spatial diversity. This constraint reduces beamforming gain and significantly impairs RSMA performance. To address this problem, we propose a movable antenna (MA)-aided RSMA scheme that allows the antennas at the base station (BS) to dynamically adjust their positions. Our objective is to maximize the system sum rate of common and private messages by jointly optimizing the MA positions, beamforming matrix, and common rate allocation. To tackle the formulated non-convex problem, we apply fractional programming (FP) and develop an efficient two-stage, coarse-to-fine-grained searching (CFGS) algorithm to obtain high-quality solutions. Numerical results demonstrate that, with optimized antenna adjustments, the MA-enabled system achieves substantial performance and reliability improvements in RSMA over fixed-position antenna setups.