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 $e^+e^- to h gamma$: $sigma_{hgamma}^L <$ 1.8 fb and $sigma_{hgamma}^R <$ 0.5 fb respectively for left- and right-handed polarisations. The constraints on effective $hgamma Z$ couplings are to be further studied.
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