This paper presents a measurement of the polarisation of tau leptons produced in Z/gamma* -> tau tau decays which is performed with a dataset of proton-proton collisions at root 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/gamma* -> tau tau decays are reconstructed from a hadronically decaying tau lepton with a single charged particle in the final state, accompanied by a tau lepton that decays leptonically. The tau polarisation is inferred from the relative fraction of energy carried by charged and neutral hadrons in the hadronic tau decays. The polarisation is measured in a fiducial region that corresponds to the kinematic region accessible to this analysis. The tau polarisation extracted over the full phase space within the Z/gamma* mass range of 66 < mZ/gamma* < 116GeVis found to be P-tau = -0.14 +/- 0.02(stat)+/- 0.04(syst). It is in agreement with the Standard Model prediction of Pt = -0.1517 +/- 0.0019, which is obtained from the ALP-GEN event generator interfaced with the PYTHIA 6 parton shower modelling and the TAUOLA tau decay library.