  In this paper we investigate the properties of astrometric microlensing of
distant radio sources (QSOs and radio galaxies) due to MACHOs, and discuss
their implications for VERA (VLBI Exploration of Radio Astrometry). First we
show that in case of astrometric microlensing of distant sources, the event
duration is only a function of the lens mass and tangential velocity, but
independent of the lens distance, in contrast to the well-known three-fold
degeneracy for photometric microlensing. Moreover, the lens mass $M$ is scaled
by the tangential velocity $v_\perp$ as $M\propto v_\perp$, rather than
$M\propto v_\perp^2$ which is the case for photometric microlensing. Thus, in
astrometric microlensing the dependence of the lens mass on the unknown
parameter $v_\perp$ is weaker, indicating that the duration of astrometric
microlensing event is a better quantity to study the mass of lensing objects
than that of photometric microlensing. We also calculate the optical depth and
event rate, and show that within 20$^\circ$ of the galactic center a typical
event rate for 10 $\mu$as-level shift is larger than $2.5 \times 10^{-4}$ event
per year, assuming that a quarter of the halo is made up with MACHOs. This
indicates that if one monitors a few hundred sources for $\sim$20 years, such
an astrometric microlensing event is detectable. Since a typical event duration
is found to be fairly long (5 to 15 years), the frequency of the monitoring
observation can be relatively low, i.e., once per six months, which is rather
reasonable for practical observations. We discuss practical strategy for
observing astrometric microlensing with VERA, and argue that an astrometric
microlensing event due to MACHOs can be detected by VERA within a few decades.
