  Motion of a test particle plays an important role in understanding the
properties of a spacetime. As a new type of the strong gravity system, boson
stars could mimic black holes located at the center of galaxies. Studying the
motion of a test particle in the spacetime of a rotating boson star will
provide the astrophysical observable effects if a boson star is located at the
center of a galaxy. In this paper, we investigate the timelike geodesic of a
test particle in the background of a rotating boson star with angular number
$m=(1, 2, 3)$. With the change of angular number and frequency, a rotating
boson star will transform from the low rotating state to the highly
relativistic rapidly rotating state, the corresponding Lense-Thirring effects
will be more and more significant and it should be studied in detail. By
solving the four-velocity of a test particle and integrating the geodesics, we
investigate the bound orbits with a zero and nonzero angular momentum. We find
that a test particle can stay more longer time in the central region of a boson
star when the boson star becomes from low rotating state to highly relativistic
rotating state. Comparing the periapse values of the orbits obtained in
rotating boson stars and the corresponding orbits of the observed stars
orbiting Sagittarius $A^*$, we discuss the possible observable effects of the
astrophysical boson star in the Galactic center.
