Within the paradigm of warped extra dimensions, third generation quarks are expected to be the most sensitive to effects beyond the Standard Model. The anomalies observed at the LEP and Tevatron colliders in the forward-backward asymmetries of the bottom (A_FB^b) and top (A_FB^t) quarks can thus be seen as early signatures of warped extra-dimensional scenarios. We propose a realization of such a scenario, with a gauge custodial symmetry in the bulk, which allows to address simultaneously the A_FB^b anomaly and the discrepancies observed recently on A_FB^t at high top quark rapidities and ttbar invariant masses. We also show that the various phenomenological constraints arising from LEP, Tevatron and LHC can be satisfied within the considered model. The model predicts new features, induced by a Kaluza-Klein excitation of the gluon at a mass ~1.5-2 TeV, in top quark pair production at the 7 TeV LHC.