Deep learning-based super-resolution (SR) usually does not perform well across domains, e.g., different Magnetic Resonance Imaging datasets, usually due to two reasons: 1) a mismatch in terms of data distributions between the training data and test data, and 2) the overly simple image degradation lacks modelling of the underlying physical processes. Hence, SR currently requires extensive fine tuning for every target domain including access to samples from the source domain. We propose UTAR, a source-free a source-free Unsupervised Test-time domain Adaptation framework for deep learning-based super-resolution for magnetic Resonance imaging. UTAR improves the quality of predicted high-resolution (HR) images from unseen target domain low-resolution (LR) images. We adapted a pre-trained SR model without re-accessing the source domain data. Our method is generic and can be used as a plug-in module in general SR networks. Experimental results verify the effectiveness of UTAR in reducing the performance gap without extensive adaption. We expect our method to provide a key step towards the deployment of MRI SR algorithms in clinical applications where significant domain shifts are inevitable.