© 2019 The American Astronomical Society. All rights reserved. Given the absence of directly detected dark matter (DM) as weakly interacting massive particles, there is strong interest in the possibility that DM is an ultralight scalar field, here denoted as "fuzzy" DM. Ultra-diffuse galaxies, with the sizes of giant galaxies and the luminosities of dwarf galaxies, have a wide range of DM halo masses, thus providing new opportunities for exploring the connections between galaxies and their DM halos. Following up on new integral field unit spectroscopic observations and dynamics modeling of the DM-dominated ultra-diffuse galaxy Dragonfly 44 in the outskirts of the Coma Cluster, we present models of fuzzy DM constrained by the stellar dynamics of this galaxy. We infer a scalar field mass of ∼ 3 × 10-22 eV, consistent with other constraints from galaxy dynamics but in tension with constraints from Lyα forest power spectrum modeling. While we are unable to statistically distinguish between fuzzy DM and "normal" cold DM models, we find that the inferred properties of the fuzzy DM halo satisfy a number of predictions for halos in a fuzzy DM cosmology. In particular, we find good agreement with the predicted core size-halo mass relation and the predicted transition radius between the quantum pressure-dominated inner region and the outer halo region.