We present spatially-resolved stellar kinematics of the well-studied ultra diffuse galaxy ( UDG ) Dragonfly 44 , as determined from 25.3 hrs of observations with the Keck Cosmic Web Imager . The luminosity-weighted dispersion within the half-light radius is \sigma _ { 1 / 2 } = 33 ^ { +3 } _ { -3 } km s ^ { -1 } , lower than what we had inferred before from a DEIMOS spectrum in the H \alpha region . There is no evidence for rotation , with V _ { max } / \langle { } \sigma \rangle < 0.12 ( 90 % confidence ) along the major axis , in possible conflict with models where UDGs are the high-spin tail of the normal dwarf galaxy distribution . The spatially-averaged line profile is more peaked than a Gaussian , with Gauss-Hermite coefficient h _ { 4 } = 0.13 \pm 0.05 . The mass-to-light ratio within the effective radius is ( M _ { dyn } / L _ { I } ) ( < R _ { e } ) = 26 ^ { +7 } _ { -6 } M _ { \odot } / L _ { \odot } , similar to other UDGs and higher by a factor of six than smaller galaxies of the same luminosity . This difference between UDGs and other galaxies is , however , sensitive to the aperture that is used , and is much reduced when the M / L ratios are measured within a fixed radius of 10 kpc . Dragonfly 44 has a rising velocity dispersion profile , from \sigma = 26 ^ { +4 } _ { -4 } km s ^ { -1 } at R = 0.2 kpc to \sigma = 41 ^ { +8 } _ { -8 } km s ^ { -1 } at R = 5.1 kpc . The profile can only be fit with a cuspy NFW profile if the orbital distribution has strong tangential anisotropy , with \beta = -0.8 ^ { +0.4 } _ { -0.5 } . An alternative explanation is that the dark matter profile has a core : a Di Cintio et al . ( 2014 ) density profile with a mass-dependent core provides a very good fit to the kinematics for a halo mass of \log ( M _ { 200 } / { M } _ { \odot } ) = 11.2 ^ { +0.6 } _ { -0.6 } and \beta = -0.1 ^ { +0.2 } _ { -0.3 } , i.e . isotropic orbits . This model predicts a slight positive kurtosis , in qualitative agreement with the measured h _ { 4 } parameter . UDGs such as Dragonfly 44 are dark matter dominated even in their centers , and can constrain the properties of dark matter in a regime where baryons usually dominate the kinematics : small spatial scales in massive halos . In a companion paper ( Wasserman et al . 2019 ) we provide constraints on the axion mass in the context of ‘ ‘ fuzzy ’ ’ dark matter models .