This paper presents a measurement of the polarisation of τ leptons produced in Z/ γ∗→ ττ decays which is performed with a dataset of proton—proton collisions at s=8 TeV, corresponding to an integrated luminosity of 20.2 fb- 1 recorded with the ATLAS detector at the LHC in 2012. The Z/ γ∗→ ττ decays are reconstructed from a hadronically decaying τ lepton with a single charged particle in the final state, accompanied by a τ lepton that decays leptonically. The τ polarisation is inferred from the relative fraction of energy carried by charged and neutral hadrons in the hadronic τ decays. The polarisation is measured in a fiducial region that corresponds to the kinematic region accessible to this analysis. The τ polarisation extracted over the full phase space within the Z/ γ∗ mass range of 66 <mZ/ 116 GeV is found to be Pτ= - 0.14 ± 0.02 (stat) ± 0.04 (syst). It is in agreement with the Standard Model prediction of Pτ= - 0.1517 ± 0.0019 , which is obtained from the ALPGEN event generator interfaced with the PYTHIA 6 parton shower modelling and the TAUOLA τ decay library.