  We investigate properties of astrometric microlensing of distant sources
(such as QSOs and radio galaxies) caused by stars in the Galaxy, mainly
focusing on application to the VERA (VLBI Exploration of Radio Astrometry)
project. Assuming typical parameters for the Galaxy disk and bulge, we show
that the maximum optical depth for astrometric shift of 10 micro-arcsec level
is 8.9x10^{-2} for QSO-disk lensing case and 3.8x10^{-2} for QSO-bulge lensing
case. We also find that the maximum optical depth for QSO-disk lensing is
larger by an order of magnitude than that for disk-disk or bulge-disk lensing
case (assuming a typical source distance of 8 to 10 kpc). In addition to
optical depth, we also calculate the event rate and find that the maximum event
rate for QSO-disk lensing case is 1.2x10^{-2} event per year, which is about 30
times greater than that for disk-disk lensing case. This high event rate
implies that if one monitors 10 QSOs behind the Galactic center region for 10
years, at least one astrometric microlensing event should be detected.
Therefore, monitoring distant radio sources with VERA can be a new tool to
study astrometric microlensing caused by stars in the Galaxy. We discuss the
implications of astrometric microlensing for VERA by focusing on estimating the
lens mass, and also present some possible candidates of radio sources toward
which astrometric microlensing events should be searched for with VERA.
(abridged)

Astrophysics