  Small-scale dark matter structures lighter than a billion solar masses are an
important probe of primordial density fluctuations and dark matter
microphysics. Due to their lack of starlight emission, their only guaranteed
signatures are gravitational in nature. We report on results of a search for
astrometric weak lensing by compact dark matter subhalos in the Milky Way with
Gaia DR3 data. Using a matched-filter analysis to look for correlated imprints
of time-domain lensing on the proper motions of background stars in the
Magellanic Clouds, we exclude order-unity substructure fractions in halos with
masses $M_{l}$ between $10^{7} \, M_{\odot}$ and $10^{9} \, M_{\odot}$ and
sizes of one parsec or smaller. We forecast that a similar approach based on
proper accelerations across the entire sky with data from Gaia DR4 may be
sensitive to substructure fractions of $f_{l} \gtrsim 10^{-3}$ in the much
lower mass range of $10 \, M_{\odot} \lesssim M_{l} \lesssim 3 \times 10^{3} \,
M_{\odot}$. We further propose an analogous technique for stacked star-star
lensing events in the regime of large impact parameters. Our first
implementation is not yet sufficiently sensitive but serves as a useful
diagnostic and calibration tool; future data releases should enable average
stellar mass measurements using this stacking method.
