We investigate properties of astrometric microlensing of distant sources (such as quasi-stellar objects [QSOs] and radio galaxies) caused by stars in the Galaxy, mainly focusing on application of the VERA (VLBI Exploration of Radio Astrometry) project. Assuming typical parameters for the Galactic disk and bulge, we show that the maximum optical depth for astrometric shift of the 10 μas level is 8.9 × 10^-2 for the QSO-disk lensing case and 3.8 × 10^-2 for the 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 (assuming a typical source distance of 8-10 kpc). In addition to optical depth, we also calculate the event rate and find that the maximum event rate for the QSO-disk lensing case is 1.2 × 10^-2 events yr^-1, which is about 30 times greater than that for disk-disk lensing. This high event rate implies that if one monitors 10 QSOs behind the Galactic center region for 10 yr, 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 also study the event duration of astrometric microlensing and find that the mean event duration for QSO-disk lensing is 7.5 yr for QSOs located near the Galactic center. This event duration for QSO-disk lensing is reasonably short compared to the project lifetime of VERA, which is anticipated to be ~20 yr. We also find that while the minimum event duration for bulge-bulge lensing is as short as 2.6 yr, the event duration for disk-disk lensing cannot be shorter than 15 yr. Thus, although astrometric microlensing of bulge sources/lenses can be studied by optical astrometric missions like SIM and GAIA, detections of disk events with the space astrometric missions are fairly difficult because of the limited project lifetime (typically ~5 yr) as well as the heavy dust extinction. Therefore, for studying astrometric microlensing by disk stars, VERA can be a powerful tool based on observations of distant sources like QSOs and radio galaxies. We discuss the implications of astrometric microlensing for VERA by focusing on estimating the lens mass, and we also present some possible candidates of radio sources toward which astrometric microlensing events should be searched for with VERA.