  Future space-borne gravitational-wave detectors will observe the
gravitational waves in the milli-Hz. Extreme-mass-ratio inspirals with central
supermassive black holes are very important sources that could provide the
information of the vicinity of black holes. The event horizon separates the
inner region of a black hole and there is nothing that can escape from this
region. When the central supermassive compact object is a regular and
horizonless rotating boson star, a small body could pass through the center and
follow novel types of orbits. These will generate the gravitational waves that
can not be obtained in the scenario corresponding to an extreme-mass-ratio
inspiral with a central supermassive black hole. This can be used to examine
whether a supermassive rotating boson star is present at the centers of
galaxies. In this work, we consider an extreme-mass-ratio inspiral system
described by a small compact object inspiralling into a central supermassive
rotating boson star. Integrating four types of special equatorial geodesics and
using the numerical kludge method with quadrupole approximation, we obtain the
corresponding gravitational waveforms and find that there are high-frequency
gravitational radiation pulses in such system. The frequencies of the
gravitational radiation pulses could be in the magnitude of $10^{-1}$Hz and the
whole gravitational wave parts are in the milli-Hz. By assuming the masses of
the central supermassive rotating boson star and small compact object to be
$10^6 M_\odot$ and $10 M_\odot$ and assuming a distance of $1\text{Gpc}$, we
show that the gravitational radiation pulses could be detected by the
space-borne gravitational-wave detectors. Our results will provide a possible
evidence to distinguish the astrophysical compact objects in the galactic
centers.
