  We studied the $e^+e^- \to h \gamma $ process at the International Linear
Collider (ILC) at $\sqrt{s}=250$ GeV, based on the full detector simulation of
the International Large Detector (ILD). This process is loop-induced in the
Standard Model (SM) and is sensitive to new physics which alters $h \gamma
\gamma$ or $h \gamma Z$ coupling. We performed the analysis by employing the
leading signal channels with $h \to b \bar{b}$ and $h \to WW^*$ and including
full SM background processes. The results are obtained for two scenarios of
beam polarisations each with an integrated luminosity of 900 fb$^{-1}$. We
found the expected significance of the SM signal is 0.40$\sigma$ for
$P(e^-,e^+)=(-0.8,+0.3)$ (the left-handed polarisation), and 0.06$\sigma$ for
$P(e^-,e^+)=(+0.8,-0.3)$ (the right-handed polarisation). The bounds on new
physics effects are reported as the 95% C.L. upper limit for the cross-section
of $e^+e^- \to h \gamma$: $\sigma_{h\gamma}^L <$ 1.8 fb and $\sigma_{h\gamma}^R
<$ 0.5 fb respectively for left- and right-handed polarisations. The
constraints on effective $h\gamma Z$ couplings are to be further studied.
