  We investigate the sensitivity of a large, underground LArTPC-based neutrino
detector to dark matter in the Galactic Center annihilating into neutrinos.
Such a detector could have the ability to resolve the direction of the electron
in a neutrino scattering event, and thus to infer information about the source
direction for individual neutrino events. We consider the improvements on the
expected experimental sensitivity that this directional information would
provide. Even without directional information, we find a DUNE-like LArTPC
detector is capable of setting limits on dark matter annihilation to neutrinos
for dark matter masses above 30 MeV that are competitive with or exceed current
experimental reach. While currently-demonstrated angular resolution for
low-energy electrons is insufficient to allow any significant increase in
sensitivity, these techniques could benefit from improvements to algorithms and
the additional spatial information provided by novel 3D charge imaging
approaches. We consider the impact of such enhancements to the resolution for
electron directionality, and find that where electron-scattering events can be
distinguished from charged-current neutrino interactions, limits on dark matter
annihilation in the mass range where solar neutrino backgrounds dominate
($\lesssim 15$ MeV) can be significantly improved using directional
information, and would be competitive with existing limits using $40$
kton$\times$year of exposure.
