  Estimating the spin of ${\rm SgrA^\ast}$ is one of the current challenges we
face in understanding the center of our Galaxy. In the present work, we show
that detecting the gravitational waves (GWs) emitted by a brown dwarf
inspiraling around ${\rm SgrA^\ast}$ will allow us to measure the mass and the
spin of ${\rm SgrA^\ast}$ with unprecedented accuracy. Such systems are known
as extremely large mass-ratio inspirals (XMRIs) and are expected to be abundant
and loud sources in our galactic center. We consider XMRIs with a fixed orbital
inclination and different spins of ${\rm SgrA^\ast}$ ($s$) between 0.1 and 0.9.
For both cases, we obtain the number of circular and eccentric XMRIs expected
to be detected by space-borne GW detectors like LISA and TianQin. We find that
if the orbit is eccentric, then we expect to always have several XMRIs in band
while for almost circular XMRIs, we only expect to have one source in band if
${\rm SgrA^\ast}$ is highly spinning. We later perform a Fisher matrix analysis
to show that by detecting a single XMRI the mass of ${\rm SgrA^\ast}$ can be
determined with an accuracy of the order $10^{-2}\,\text{M}_{\odot}$, while the
spin can be measured with an accuracy between $10^{-7}$ and $10^{-4}$ depending
on the orbital parameters of the XMRI.
