  We show that electron recoils induced by non-relativistic Dark Matter
interactions can fit well the recently reported Xenon1T excess, if they are
mediated by a light pseudo-scalar in the MeV range. This is due to the
favorable momentum-dependence of the resulting scattering rate, which partially
compensates the unfavorable kinematics that tends to strongly suppress keV
electron recoils. We study the phenomenology of the mediator and identify the
allowed parameter space of the Xenon1T excess which is compatible with all
experimental limits. We also find that the anomalous magnetic moments
$(g-2)_{\mu,e}$ of muons and electrons can be simultaneously explained in this
scenario, at the prize of a fine-tuning in the couplings of the order of a few
percent.
