This letter presents a measurement of the top quark pair (tt) production charge asymmetry Ac using 4.7 fb-1 of proton-proton collisions at a centre-of-mass energy of 7 TeV collected by the ATLAS detector at the LHC. A tt-enriched sample of events with a single lepton (electron or muon), missing transverse momentum and at least four high transverse momentum jets, of which at least one is tagged as coming from a b-quark, is selected. A likelihood fit is used to reconstruct the tt event kinematics. A Bayesian unfolding procedure is employed to estimate Ac at the parton-level. The measured value of the tt production charge asymmetry is 0.006 +/- 0.010, where the uncertainty includes both the statistical and the systematic components. Differential Ac measurements as a function of the invariant mass, the rapidity and the transverse momentum of the tt-system are also presented. In addition, Ac is measured for a subset of events with large tt velocity, where physics beyond the Standard Model could contribute. All measurements are consistent with the Standard Model predictions.