  One of remarkable features of loop quantum gravity (LQG) is that it can
provide resolutions to both the black hole and big bang singularities. In the
mini-superspace approach based on the polymerization procedure in LQG, a
quantum corrected black hole metric is constructed. This metric is also known
as self-dual spacetime since the form of the metric is invariant under the
exchange $r \to a_0/r$ with $a_0$ being proportional to the minimum area in LQG
and $r$ is the standard radial coordinate at asymptotic infinity. It modifies
the Schwarzschild spacetime by the polymeric function $P$, purely due to the
geometric quantum effects from LQG. Here $P$ is related to the polymeric
parameter $\delta$ which is introduced to define the paths one integrates the
connection along to define the holonomies in the quantum corrected Hamiltonian
constraint in the polymerization procedure in LQG. In this paper, we consider
its effects on the orbital signatures of S0-2 star orbiting Sgr A* in the
central region of our Milky Way, and compare it with the publicly available
astrometric and spectroscopic data, including the astrometric positions, the
radial velocities, and the orbital precession for the S0-2 star. We perform
Monte Carlo Markov Chain (MCMC) simulations to probe the possible LQG effects
on the orbit of S0-2 star. No significant evidence of the self-dual spacetime
arisIng from LQG is found. We thus place an upper bounds at 95\% confidence
level on the polymeric function $P < 0.043$ and $P < 0.056$, for Gaussian and
uniform priors on orbital parameters, respectively.
