A test of CP invariance in Higgs boson production via vector-boson fusion is performed in the H -> tau tau decay channel. This test uses the Optimal Observable method and is carried out using 36.1 fb(-1) of root s = 13 TeV proton-proton collision data collected by the ATLAS experiment at the LHC. Contributions from CP-violating interactions between the Higgs boson and electroweak gauge bosons are described by an effective field theory, in which the parameter (d) over tilde governs the strength of CP violation. No sign of CP violation is observed in the distributions of the Optimal Observable, and (d) over tilde is constrained to the interval [-0.090, 0.035] at the 68% confidence level (CL), compared to an expected interval of (d) over tilde is an element of [ -0.035, 0.033] based upon the Standard Model prediction. No constraints can be set on (d) over tilde at 95% CL, while an expected 95% CL interval of (d) over tilde is an element of [ -0.21, 0.15] for the Standard Model hypothesis was expected.