  We study the $e^+e^-\to h \gamma$ process at the International Linear
Collider (ILC) to probe new physics in the $h\gamma Z$ coupling. The study is
performed at a center of mass energy of 250 GeV and is based on the full
simulation of the International Large Detector (ILD). The expected signal
significance is found to be 0.53 $\sigma$ for an integrated luminosity of 2000
fb$^{-1}$ in the case of the standard model. The corresponding 95 $\%$
confidence level upper limit for the signal cross section is 1.08 fb for
left-handed beam polarization.
