Vision Transformer (ViT) has become a state-of-art in many vision tasks, owing to its great scalability and promising performance. In Magnetic Resonance Imaging (MRI), motion continues to be a major problem, which degrades the image quality and the corresponding disease assessment. The purpose of this work is to assess a ViT-based MRI motion correction method. Self-supervised learning was further incorporated to enhance the motion correction effects. Training image pairs were generated starting with in-house MRI data of high quality, from which simulated images with artifacts were generated using a k-space resampling algorithm based on real head movements. We randomly mask 50% patches of the input image and reconstruct the missing pixels as self-supervised pre-training to boost performance of the ViT model. The output images of the proposed method from motion-corrupted data had significantly improved image quality compared with the original corrupted images and are better than the results of a previous deep learning-based motion correction algorithm: the UNet-based MC-Net and a baseline ViT based method in terms of quantitative metrics. This study offers a practical approach for elimination of motion artifacts from brain MRI, using self-supervised learning and ViT.