High-resolution (HR) magnetic resonance imaging (MRI) is crucial for enhancing diagnostic accuracy in clinical settings. Nonetheless, the inherent limitation of MRI resolution restricts its widespread applicability. Deep learning-based image super-resolution (SR) methods exhibit promise in improving MRI resolution without additional cost. However, these methods frequently require a substantial number of HR MRI images for training, which can be challenging to acquire. In this paper, we propose an unpaired MRI SR approach that employs self-supervised contrastive learning to enhance SR performance with limited training data. Our approach leverages both authentic HR images and synthetically generated SR images to construct positive and negative sample pairs, thus facilitating the learning of discriminative features. Empirical results presented in this study underscore significant enhancements in the peak signal-to-noise ratio and structural similarity index, even when a paucity of HR images is available. These findings accentuate the potential of our approach in addressing the challenge of limited training data, thereby contributing to the advancement of high-resolution MRI in clinical applications.