Diffusion magnetic resonance imaging (dMRI) provides unique capabilities for non-invasive mapping of fiber tracts in the brain. It however suffers from relatively low spatial resolution, often leading to partial volume effects. In this paper, we propose to use a super-resolution approach based on dictionary learning for alleviating this problem. Unlike the majority of existing super-resolution algorithms, our proposed solution does not entail acquiring multiple scans from the same subject which renders it practical in clinical settings and applicable to legacy data. Moreover, this approach can be used in conjunction with any diffusion model. Motivated by how functional connectivity (FC) reflects the underlying structural connectivity (SC), we quantitatively validate our results by investigating the consistency between SC and FC before and after super-resolving the data. Based on this scheme, we show that our method outperforms traditional interpolation strategies and the only existing single image super-resolution method for dMRI that is not dependent on a specific diffusion model. Qualitatively, we illustrate that fiber tracts and tract-density maps reconstructed from super-resolved dMRI data reveal exquisite details beyond what is achievable with the original data.