This paper reports inclusive and differential measurements of the t (t) over bar charge asymmetry A(C) in 20.3 fb(-1) of root s = 8 TeV pp collisions recorded by the ATLAS experiment at the Large Hadron Collider at CERN. Three differential measurements are performed as a function of the invariant mass, transverse momentum and longitudinal boost of the t (t) over bar system. The t (t) over bar pairs are selected in the single-lepton channels (e or mu) with at least four jets, and a likelihood fit is used to reconstruct the t (t) over bar event kinematics. A Bayesian unfolding procedure is performed to infer the asymmetry at parton level from the observed data distribution. The inclusive t (t) over bar charge asymmetry is measured to be A(C) = 0.009 +/- 0.005 (stat. + syst.). The inclusive and differential measurements are compatible with the values predicted by the Standard Model.