  The Event Horizon Telescope (EHT) collaboration's image of the compact object
at the galactic center is the first direct evidence of the supermassive black
hole (BH) Sgr A$^*$. The shadow of Sgr A$^*$ has an angular diameter $d_{sh}=
48.7 \pm 7\,\mu$as with fractional deviation from the Schwarzschild BH shadow
diameter $\delta= -0.08^{+0.09}_{-0.09}\,,-0.04^{+0.09}_{-0.10}$ (for the VLTI
and Keck mass-to-distance ratios). Sgr A$^*$'s shadow size is within $~10\%$ of
Kerr predictions, equipping us with yet another tool to analyze gravity in the
strong-field regime, including testing loop quantum gravity (LQG). We use Sgr
A$^*$'s shadow to constrain the metrics of two well-motivated LQG-inspired
rotating BH (LIRBH) models characterized by an additional deviation parameter
$L_q$, which recover the Kerr spacetime in the absence of quantum effects ($L_q
\to 0$). When increasing the quantum effects through $L_q$, the shadow size
increases monotonically, while the shape gets more distorted, allowing us to
constrain the fundamental parameter $L_q$. We use the astrophysical observables
shadow area $A$ and oblateness $D$ to estimate the BH parameters. It may be
useful in extracting additional information about LIRBHs. While the EHT
observational results completely rule out the wormhole region in the LIRBH-2, a
substantial parameter region of the generic BHs in both models agrees with the
EHT results. We find that the upper bounds on $L_q$ obtained from the shadow of
Sgr A$^*$ -- $L_q \lesssim 0.0423$ and $L_q \lesssim 0.0821$ for the two
LIRBHs, respectively -- are more stringent than those obtained from the EHT
image of M87$^*$.
