Higgs boson production in association with a hard central photon and two forward tagging jets is expected to provide valuable information on Higgs boson couplings in a range where it is difficult to disentangle weak-boson fusion processes from large QCD backgrounds. We present next-to-leading order QCD corrections to Higgs production in association with a photon via weak-boson fusion at a hadron collider in the form of a flexible parton-level Monte Carlo program. The QCD corrections to integrated cross sections are found to be small for experimentally relevant selection cuts, while the shape of kinematic distributions can be distorted by up to 20% in some regions of phase space. Residual scale uncertainties at next-to-leading order are at the few-percent level.