  Dark matter phenomena in rotationally supported galaxies exhibit a
characteristic acceleration scale of $g_\dagger \approx 1.2\times 10^{-10}$ m
s$^{-2}$. Whether this acceleration is a manifestation of a universal scale, or
merely an emergent property with an intrinsic scatter, has been debated in the
literature. Here we investigate whether a universal acceleration scale exists
in dispersion-supported galaxies using two uniform sets of integral field
spectroscopy (IFS) data from SDSS-IV MaNGA and ATLAS$^{\rm 3D}$. We apply the
spherical Jeans equation to 15 MaNGA and 4 ATLAS$^{\rm 3D}$ slow-rotator E0
(i.e., nearly spherical) galaxies. Velocity dispersion profiles for these
galaxies are well determined with observational errors under control. Bayesian
inference indicates that all 19 galaxies are consistent with a universal
acceleration of $g_\dagger=1.5_{-0.6}^{+0.9}\times 10^{-10}$ m s$^{-2}$.
Moreover, all 387 data points from the radial bins of the velocity dispersion
profiles are consistent with a universal relation between the radial
acceleration traced by dynamics and that predicted by the observed distribution
of baryons. This universality remains if we include 12 additional non-E0
slow-rotator elliptical galaxies from ATLAS$^{\rm 3D}$. Finally, the universal
acceleration from MaNGA and ATLAS$^{\rm 3D}$ is consistent with that for
rotationally supported galaxies, so our results support the view that dark
matter phenomenology in galaxies involves a universal acceleration scale.
