  Astrometric weak gravitational lensing is a powerful probe of the
distribution of matter on sub-Galactic scales, which harbor important
information about the fundamental nature of dark matter. We propose a novel
method that utilizes angular power spectra to search for the correlated pattern
of apparent motions of celestial objects induced from time-dependent lensing by
a population of Galactic subhalos. Application of this method to upcoming
astrometric datasets will allow for the direct measurement of the properties of
Galactic substructure, with implications for the underlying particle physics.
We show that, with near-future astrometric observations, it may be possible to
statistically detect populations of cold dark matter subhalos, compact objects,
as well as density fluctuations sourced by scalar field dark matter.
Currently-unconstrained parameter space will already be accessible using
upcoming data from the ongoing Gaia mission.
