Accurate tissue motion tracking is critical to ensure treatment outcome and safety in 2D-Cine MRI-guided radiotherapy. This is typically achieved by registration of sequential images, but existing methods often face challenges with large misalignments and lack of interpretability. In this paper, we introduce DINOMotion, a novel deep learning framework based on DINOv2 with Low-Rank Adaptation (LoRA) layers for robust, efficient, and interpretable motion tracking. DINOMotion automatically detects corresponding landmarks to derive optimal image registration, enhancing interpretability by providing explicit visual correspondences between sequential images. The integration of LoRA layers reduces trainable parameters, improving training efficiency, while DINOv2's powerful feature representations offer robustness against large misalignments. Unlike iterative optimization-based methods, DINOMotion directly computes image registration at test time. Our experiments on volunteer and patient datasets demonstrate its effectiveness in estimating both linear and nonlinear transformations, achieving Dice scores of 92.07% for the kidney, 90.90% for the liver, and 95.23% for the lung, with corresponding Hausdorff distances of 5.47 mm, 8.31 mm, and 6.72 mm, respectively. DINOMotion processes each scan in approximately 30ms and consistently outperforms state-of-the-art methods, particularly in handling large misalignments. These results highlight its potential as a robust and interpretable solution for real-time motion tracking in 2D-Cine MRI-guided radiotherapy.