Many clinical applications require medical image harmonization to combine and normalize images from different scanners or protocols. This paper introduces a Transformer-based MR image harmonization method. Our proposed method leverages the self-attention mechanism of the Transformer to learn the complex relationships between image patches and effectively transfer the imaging characteristics from a source image domain to a target image domain. We evaluate our approach to state-of-the-art methods using a publicly available dataset of brain MRI scans and show that it provides superior quantitative metrics and visual quality. Furthermore, we demonstrate that the proposed approach is highly resistant to fluctuations in image modality, resolution, and noise. Overall, the experiment results indicate that our approach is a promising method for medical image harmonization that can improve the accuracy and reliability of automated analysis and diagnosis in clinical settings.