A planet orbiting a radio-emitting star can be indirectly detected by high-precision very long baseline interferometry (VLBI) astrometry through the reflex orbit of the star. We have observed the radio-emitting star &sgr;2 CrB at 15 epochs over 7.5 years by VLBI and fitted its five astrometric parameters to the measured VLBI coordinates. The postfit coordinate residuals have an rms scatter of 0.33 milliarcsecond (mas) when all 15 epochs are used. However, when only the seven epochs at which the star was in its radio quiescent regime are used, the postfit rms drops to 0.20 mas, indicating that the radio centroid is more stable than during outbursts. The systematic errors in these VLBI astrometric observations are estimated to be 0.1 mas only. The larger rms scatter found (0.20 mas) might be caused by either a random jitter of the radio source or a planetary perturbation that is not sampled sufficiently to be recognized by visual inspection of the postfit position residuals. This will be tested by more frequent VLBI observations of this star in the future. Finally, the theoretical (signal-to-noise ratio-limited) astrometric precision of VLBI observations of radio-emitting stars is ~10 μarc sec and corresponds to an interesting limit to search for giant planets around stars up to 200 pc and even for an Earth-like planet but around the nearest radio-emitting star UV Ceti. ¿ American Geophysical Union 1996