Dark matter phenomena in rotationally supported galaxies exhibit a characteristic acceleration scale of $g_dagger approx 1.2times 10^{-10}$ 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.
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