A test of CP invariance in Higgs boson production via vector-boson fusion is performed in the $H\to \tau \tau$ decay channel. This test uses the Optimal Observable method and is carried out using 36.1 $\mathrm{fb}-1$ of $s$ = 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 $d~$ governs the strength of CP violation. No sign of CP violation is observed in the distributions of the Optimal Observable, and $d~$ is constrained to the interval $[-0.090,0.035]$ at the 68% confidence level (CL), compared to an expected interval of $d~\in [-0.035,0.033]$ based upon the Standard Model prediction. No constraints can be set on $d~$ at 95% CL, while an expected 95% CL interval of $d~\in [-0.21,0.15]$ for the Standard Model hypothesis was expected.