This Letter presents measurements of the polarization of the top quark in top-antitop quark pair events, using 4.7 fb(-1) of proton-proton collision data recorded with the ATLAS detector at the Large Hadron Collider at √s=7 TeV. Final states containing one or two isolated leptons (electrons or muons) and jets are considered. Two measurements of α(ℓ)P, the product of the leptonic spin-analyzing power and the top quark polarization, are performed assuming that the polarization is introduced by either a CP conserving or a maximally CP violating production process. The measurements obtained, α(ℓ)P(CPC)=-0.035±0.014(stat)±0.037(syst) and α(ℓ)P(CPV)=0.020±0.016(stat)(-0.017)(+0.013)(syst), are in good agreement with the standard model prediction of negligible top quark polarization.