This paper presents a measurement of the top quark pair () production charge asymmetry A (C) using 4.7 fb(-1) of proton-proton collisions at a centre-of-mass energy root s = 7 TeV collected by the ATLAS detector at the LHC. A -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 event kinematics. A Bayesian unfolding procedure is employed to estimate A (C) at the parton-level. The measured value of the production charge asymmetry is A (C) = 0.006 +/- 0.010, where the uncertainty includes both the statistical and the systematic components. Differential A (C) measurements as a function of the invariant mass, the rapidity and the transverse momentum of the system are also presented. In addition, A (C) is measured for a subset of events with large velocity, where physics beyond the Standard Model could contribute. All measurements are consistent with the Standard Model predictions.