Cardiac Cine MRI is limited by prolonged acquisition times and motion-related artifacts. Existing deep learning-based reconstruction methods typically depend on fully-sampled ground truth, which is often difficult to acquire in practice. In this work, we propose SSL-MoCo, a fully self-supervised motion-compensated reconstruction framework for cardiac Cine MRI that eliminates the need for fully-sampled references. SSL-MoCo adopts a two-stage design: a transformer-based registration network estimates non-rigid inter-frame motion in a self-supervised manner, followed by a physics-based unrolled reconstruction network that integrates the estimated motion fields in the data consistency steps. Evaluations on an in-house dataset of 120 subjects (including 82 patients) demonstrate that SSL-MoCo significantly outperforms other self-supervised methods, particularly during challenging systolic phases. The integrated motion compensation enhances temporal coherence, resulting in more accurate myocardial morphology, which is crucial for clinical functional assessment. Our results suggest that SSL-MoCo provides an effective solution for dynamic MRI reconstruction in data-constrained settings.