In this paper, a measurement of tau polarization in W -> tau nu decays is presented. It is measured from the energies of the decay products in hadronic tau decays with a single final state charged particle. The data, corresponding to an integrated luminosity of 24 pb(-1), were collected by the ATLAS experiment at the Large Hadron Collider in 2010. The measured value of the tau polarization is P-tau = -1.06 +/- 0.04 (stat)(-0.07)(+0.05) (syst), in agreement with the Standard Model prediction, and is consistent with a physically allowed 95 % CL interval [-1,-0.91]. Measurements of tau polarization have not previously been made at hadron colliders.