  In this study, we investigate the process $pp \rightarrow W^{\pm} \gamma$ for
the physics potential of the FCC-hh with $\sqrt{s}=100$ TeV to examine the
anomalous $WW\gamma$ couplings defined by three CP-conserving and two
CP-violating effective operators of dimension-6. The analysis containing the
realistic detector effects is carried out in the mode where $W^{\pm}$ bosons in
the final state decay into the leptonic channel. The best sensitivities
obtained from the process $pp \rightarrow W^{\pm} \gamma$ on the anomalous
couplings $C_{WWW}/ \Lambda^{2}$ and $C_{W,B}/ \Lambda^{2}$ determined by
CP-conserving effective Lagrangians are $[-0.01; 0.01]$ TeV$^{-2}$ and $[-0.88;
0.88]$ TeV$^{-2}$, while $C_{\tilde{W}WW}/ \Lambda^{2}$ and $C_{\tilde{W}}/
\Lambda^{2}$ couplings defined by CP-violating effective Lagrangian are
obtained as $[-0.03; 0.03]$ TeV$^{-2}$ and $[-0.47; 0.47]$ TeV$^{-2}$ at the
FCC-hh with $\sqrt{s}=100$ TeV, $L_{int}=30$ ab$^{-1}$. However, if the
systematic uncertainty is included, we obtain reduced sensitivities on the
anomalous $WW\gamma$ coupling . The results are compared for assumed
systematics of $5\%$ and $10\%$.
