  The self-dual spacetime was derived from the mini-superspace approach, based
on the polymerization quantization procedure in loop quantum gravity (LQG). Its
deviation from the Schwarzschild spacetime is characterized by the polymeric
function $P$, purely due to the geometric quantum effects from LQG. In this
paper, we consider the observational constraints imposed on $P$ by using the
solar system experiments and observations. For this purpose, we calculate in
detail the effects of $P$ on astronomical observations conducted in the Solar
system, including the deflection angle of light by the Sun, gravitational time
delay, perihelion advance, and geodetic precession. The observational
constraints are derived by confronting the theoretical predictions with the
most recent observations. Among these constraints, we find that the tightest
one comes from the measurement of the gravitational time delay by the Cassini
mission, which yields $0<P<5.5\times 10^{-6}$. In addition, we also discuss the
potential constraint that can be obtained in the near future by the joint
European-Japanese BepiColombo project and show that it could significantly
improve the current constraints.
