Clinical MRI frequently acquires anisotropic volumes with high in-plane resolution and low through-plane resolution to reduce acquisition time. Multiple orientations are therefore acquired to provide complementary anatomical information. Conventional integration of these views relies on registration followed by interpolation, which can degrade fine structural details. Recent deep learning-based super-resolution (SR) approaches have demonstrated strong performance in enhancing single-view images. However, their clinical reliability is often limited by the need for large-scale training datasets, resulting in increased dependence on cohort-level priors. Self-supervised strategies offer an alternative by learning directly from the target scans. Prior work either neglects the existence of multi-view information or assumes that in-plane information can supervise through-plane reconstruction under the assumption of pre-alignment between images. However, this assumption is rarely satisfied in clinical settings. In this work, we introduce Single-Subject Implicit Multi-View Super-Resolution for MRI (SIMS-MRI), a framework that operates solely on anisotropic multi-view scans from a single patient without requiring pre- or post-processing. Our method combines a multi-resolution hash-encoded implicit representation with learned inter-view alignment to generate a spatially consistent isotropic reconstruction. We validate the SIMS-MRI pipeline on both simulated brain and clinical prostate MRI datasets. Code will be made publicly available for reproducibility: https://github.com/abhshkt/SIMS-MRI