We have tested a digital-spectroscopy-type 22-GHz water vapor radiometer (WVR) installed in one of the VERA (VLBI Exploration of Radio Astrometry) radio telescopes for directly measuring the excess path delay length (EPL) due to Earth's precipitable water vapor (PWV) towards astrometry targets (i.e. background reference and astrometry-target radio sources). Such EPL measurement is crucial to high accuracy astrometry for sources at low telescope elevations (e.g. sources in the Galactic Center observed from VERA in Japan) because the difference in the EPLs towards the targets at slightly different elevations (by degrees) may cause a non-negligible effect on astrometry at a micro-arc seconds (μas) level. Although new calibration techniques for VLBI astrometry have been developed, such as the multi-view technique, the WVR technique should be explored for millimeter VLBI astrometry, in which a coherent time for fringe visibility integration is too short for directly applying such new techniques. The WVR composed of a compact high-speed analogy-to-digital (AD) sampler can be installed on the upper cabin of the telescope. Here we present the present status of the development of the WVR technique, in which the measured EPLs shall be applied to more precise calculation of phase-tracking models used for VLBI fringe visibility calibration. The feasibility of the WVR technique will be evaluated in near future in more detail by comparison between the EPLs derived from the WVR and GPS/GNSS station data and improvement of the astrometric accuracy with applying the technique.