  High-resolution N-body simulations of dark matter halos indicate that the
Milky Way contains numerous subhalos. When a dark matter subhalo passes in
front of a star, the light from that star will be deflected by gravitational
lensing, leading to a small change in the star's apparent position. This
astrometric microlensing signal depends on the inner density profile of the
subhalo and can be greater than a few microarcseconds for an intermediate-mass
subhalo (Mvir > 10000 solar masses) passing within arcseconds of a star.
Current and near-future instruments could detect this signal, and we evaluate
SIM's, Gaia's, and ground-based telescopes' potential as subhalo detectors. We
develop a general formalism to calculate a subhalo's astrometric lensing cross
section over a wide range of masses and density profiles, and we calculate the
lensing event rate by extrapolating the subhalo mass function predicted by
simulations down to the subhalo masses potentially detectable with this
technique. We find that, although the detectable event rates are predicted to
be low on the basis of current simulations, lensing events may be observed if
the central regions of dark matter subhalos are more dense than current models
predict (>1 solar mass within 0.1 pc of the subhalo center). Furthermore,
targeted astrometric observations can be used to confirm the presence of a
nearby subhalo detected by gamma-ray emission. We show that, for sufficiently
steep density profiles, ground-based adaptive optics astrometric techniques
could be capable of detecting intermediate-mass subhalos at distances of
hundreds of parsecs, while SIM could detect smaller and more distant subhalos.
