Diffusion magnetic resonance imaging (diffusion MRI) is widely employed to probe the diffusive motion of water molecules within the tissue. Numerous diseases and processes affecting the central nervous system can be detected and monitored via diffusion MRI thanks to its sensitivity to microstructural alterations in tissue. The latter has prompted interest in quantitative mapping of the microstructural parameters, such as the fiber orientation distribution function (fODF), which is instrumental for noninvasively mapping the underlying axonal fiber tracts in white matter through a procedure known as tractography. However, such applications demand repeated acquisitions of MRI volumes with varied experimental parameters demanding long acquisition times and/or limited spatial resolution. In this work, we present a deep-learning-based approach for increasing the spatial resolution of diffusion MRI data in the form of fODFs obtained through constrained spherical deconvolution. The proposed approach is evaluated on high quality data from the Human Connectome Project, and is shown to generate upsampled results with a greater correspondence to ground truth high-resolution data than can be achieved with ordinary spline interpolation methods. Furthermore, we employ a measure based on the earth mover’s distance to assess the accuracy of the upsampled fODFs. At low signal-to-noise ratios, our super-resolution method provides more accurate estimates of the fODF compared to data collected with 8 times smaller voxel volume.