  The S-stars in the Galactic center (GC) are anticipated to provide unique
dynamical constraint on the spin of the GC massive black hole (MBH). In this
paper, we develop a fast full general relativistic method to simultaneously
constrain the MBH mass, spin, and spin direction by considering both the motion
of a star and the propagation of photons from the star to a distant observer.
Assuming some example stars, we demonstrate that the spin-induced effects on
the projected trajectory and redshift curve of a star depend on both the value
and the direction of the spin. The maximum effects over a full orbit can differ
by a factor upto more than one order of magnitude for cases with significantly
different spin directions. Adopting the Markov Chain Monte Carlo fitting
technique, we illustrate that the spin of the GC MBH is likely to be well
constrained by using the motion of S0-2/S2 over a period of ~45yr if it is
close to one and the astrometric and spectroscopic precisions (sigma_p,sigma_Z)
can be as high as (10muas, 1km/s). In the mean time, the distance from the sun
to the GC and the MBH mass can also be constrained to an unprecedented accuracy
(0.01%-0.1%). If there exists a star with semimajor axis significantly smaller
than that of S0-2/S2 and eccentricity larger than that of S0-2/S2, the MBH spin
can be constrained with high accuracy over a period of <~10yr for
(sigma_p,sigma_Z) ~ (10muas,1km/s), even if the spin is only moderately large
(>~0.2).
