  Precision astrometry offers a way to probe new physics. By measuring the
angular position of light sources at unprecedented precision, astrometry could
probe minuscule fluctuations of underlying spacetime. This work explores the
possibility of probing ultralight dark matter candidates using precision
astrometry. Through the coherent and stochastic density fluctuations over the
scale of its wavelength, ultralight dark matter perturbs the propagation of
light and the geodesics of the observer and source, leading to unique
time-dependent signatures in the angular position of background light sources.
With detector specifications similar to the current and future astrometry
observations, such as Gaia and Roman Space Telescope, it is shown that the
ultralight scalar dark matter of mass $10^{-18}\,{\rm eV} \, \textrm{--} \,
10^{-16} \,{\rm eV}$ could be probed when its density near the solar system is
about a few thousand times larger than the nominal dark matter density measured
on a much larger kpc-scale. This sensitivity is comparable to current pulsar
timing array observations at a similar mass range. Explicit expressions for the
angular deflection induced by most generic metric perturbations are derived and
its gauge invariance is explicitly checked at the linear order.
