The CP properties of the Higgs boson are studied in the vector-boson fusion production mode. The analysis exploits the decay mode of the Higgs boson into two τ-leptons using 140 fb¹ of proton-proton collision data at s=13 TeV collected by the ATLAS experiment at the Large Hadron Collider. Results are obtained using the Optimal Observable method. CP-violating interactions between the Higgs boson and electroweak gauge bosons are considered in the effective field theory framework, with the interaction strength described in the HISZ basis by d~, and in the Warsaw basis by cHW~, cHB~, and cHW~B. No deviations relative to the Standard Model are observed, and limits are obtained on the strength parameters. The d~ parameter is constrained to the interval [−0.012, 0.044] at the 95% confidence level while cHW~ is constrained to [−0.24, 0.83], when considering both linear and quadratic effects of physics beyond the Standard Model.