A measurement of the $\tau$ polarisation in $Z/\gamma^*\rightarrow\tau\tau$ decays is presented. The analysis is based on the $20.2$ fb$^{-1}$ of proton$-$proton collision data collected at a centre-of-mass energy of $\sqrt{s}=8$ TeV by the ATLAS experiment at the CERN Large Hadron Collider in 2012. Events with one leptonic $\tau$ decay and one hadronic $\tau$ decay with a single charged particle in the final state are selected. The $\tau$ polarisation is measured using the kinematic configuration of the hadronic decay. A polarisation of $P_\tau~=-0.14\;\pm~0.02\;(\textrm{stat})\;\pm~0.04\;(\textrm{syst})$ is measured in the mass range $66 < m_{Z/\gamma^*} < 116$ GeV. It agrees with the Standard Model prediction of $P_\tau~=-0.1517\pm0.0014\;(\textrm{stat})\pm0.0013\;(\textrm{syst})$.