  This paper presents a measurement of the polarisation of $\tau$ leptons
produced in $Z/\gamma^{*}\rightarrow\tau\tau$ decays which is performed with a
dataset of proton-proton collisions at $\sqrt{s}=8$ TeV, corresponding to an
integrated luminosity of 20.2 fb$^{-1}$ recorded with the ATLAS detector at the
LHC in 2012. The $Z/\gamma^{*}\rightarrow\tau\tau$ 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$ < m_{Z/\gamma^{*}} < $
116 GeV is found to be $P_{\tau} =-0.14 \pm 0.02 (\text{stat}) \pm 0.04
(\text{syst})$. It is in agreement with the Standard Model prediction of
$P_{\tau} =-0.1517 \pm 0.0019$, which is obtained from the ALPGEN event
generator interfaced with the PYTHIA 6 parton shower modelling and the TAUOLA
$\tau$ decay library.
