  Extremely precise radial velocity is essential for the detection of sub-m/s
radial velocity of stars induced by Earth-like planets. Although modeling of
the barycentric correction of radial velocity could achieve 1 mm/s precision,
the input astrometry could be biased due to nonlinear motions of stars caused
by companions. To account for astrometry-induced bias in barycentric
correction, we correct for astrometric bias by minimizing the scatter of
reduced RV data with PEXO. In particular, we apply this method to the
barycentric correction for 266 stars from HARPS data archive. We find that the
RV scatter for 8 targets are significantly reduced due to correction of
astrometric bias. Among these targets, 2 targets exhibit bias caused by known
massive companions, while for the remaining 6 targets, the bias could be
attributed to unknown companions or Gaia systematics. Furthermore, 14 targets
have an astrometry-induced annual RV variation higher than 0.05 m/s, and 10 of
them are closer than 10 pc. We show the results of Barnard's star as an
example, and find that an annual RV bias of 10 cm/s is mitigated by replacing
BarCor by PEXO as the barycentric correction code. Our work demonstrates the
necessity of astrometric bias correction and the utilization of barycentric
correction code within a relativistic framework in high-precision RV for the
detection of Earth-like planets.
