A test of CP invariance in Higgs boson production via vector-boson fusion has been performed in the H→γγ channel using 139 fb^{-1} of proton-proton collision data at sqrt[s]=13 TeV collected by the ATLAS detector at the LHC. The optimal observable method is used to probe the CP structure of interactions between the Higgs boson and electroweak gauge bosons, as described by an effective field theory. No sign of CP violation is observed in the data. Constraints are set on the parameters describing the strength of the CP-odd component in the coupling between the Higgs boson and the electroweak gauge bosons in two effective field theory bases: d[over ̃] in the HISZ basis and c_{HW[over ̃]} in the Warsaw basis. The results presented are the most stringent constraints on CP violation in the coupling between Higgs and weak bosons. The 95% C.L. constraint on d[over ̃] is derived for the first time and the 95% C.L. constraint on c_{HW[over ̃]} has been improved by a factor of 5 compared to the previous measurement.
