This paper presents a measurement of the top quark pair (t¯t) production charge asymmetry AC using 4.7 fb−1 of proton-proton collisions at a centre-of-mass energy √s = 7 TeV collected by the ATLAS detector at the LHC. A t¯t-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 t¯t event kinematics. A Bayesian unfolding procedure is employed to estimate AC at the parton-level. The measured value of the t¯t production charge asymmetry is AC = 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 t¯t- system are also presented. In addition, AC is measured for a subset of events with large t¯t velocity, where physics beyond the Standard Model could contribute. All measurements are consistent with the Standard Model predictions.