  We present results from fully general relativistic (GR), three-dimensional
(3D), neutrino-radiation magneto-hydrodynamic (MHD) simulations of stellar core
collapse of a 20 M$_\odot$ star with spectral neutrino transport. Our focus is
to study the gravitational-wave (GW) signatures from the magnetorotationally
(MR)-driven models. By parametrically changing the initial angular velocity and
the strength of the magnetic fields in the core, we compute four models. Our
results show that the MHD outflows are produced only for models (two out of
four), to which magnetic field strengths of 10$^{12}$ G and rotation rates of 1
or 2 rad s$^{-1}$ are initially imposed in the core. Seen from the direction
perpendicular to the rotational axis, a characteristic waveform is obtained
exhibiting a monotonic time increase in the wave amplitude. As previously
identified, this stems from the propagating MHD outflows along the axis. We
show that the GW amplitude from anisotropic neutrino emission becomes more than
one order-of-magnitude bigger than that from the matter contribution, whereas
seen from the rotational axis, both of the two components are in the same
order-of-magnitudes. Due to the memory effect, the frequency of the neutrino GW
from our full-fledged 3D-MHD models is in the range less than $\sim$10 Hz.
Toward the future GW detection for a Galactic core-collapse supernova, if
driven by the MR mechanism, the planned next-generation detector as DECIGO is
urgently needed to catch the low-frequency signals.
