  In this paper, we investigate the quality of constraining the spin of the
massive black hole (MBH) at the Galactic center (GC) by using full general
relativistic simulations of the motion of a surrounding star. We obtain the
dependence mapping of the spin-induced signals on any spin direction of the MBH
for given example stars, which indicates the feasibility to test whether the
spin direction is the same as the normal of the young stellar disk located at
the GC, and, further to provide insights into the assembly history of the MBH.
We demonstrate the quality of constraining the MBH spin that may be achieved,
given any set of the astrometric and the redshift precisions of observational
facilities. We find that in the ranges of the astrometric and the velocity
precisions with 1--30$\mu$as and 0.1--10 km/s, an improvement in astrometric
precision would be more effective at improving the quality of constraining the
spin than an improvement in velocity precision. We obtain the parameter space
of the semimajor axis and the eccentricity for the orbit of the target star
that a high-precision constraint on the GC MBH spin can be obtained via the
motion of the star. Our results show that the spin of the GC MBH can be
constrained with 1-sigma error <~0.1 or even >~0.02 by monitoring the orbital
motion of a star, if existing as expected, with semimajor axis <~300AU and
eccentricity >~0.95 over a period shorter than a decade through future
facilities.
