The recent Tevatron result on the top quark forward–backward asymmetry, which deviates from its standard model prediction by 3.4σ, has prompted many authors to build new models to account for this anomaly. Among the various proposals, we find that those mechanisms which produce via the t- or u-channel can have a strong correlation to the rare B decays. We demonstrate this link by studying a model with a new charged gauge boson, W′. In terms of the current measurements on B → πK decays, we conclude that the branching ratio for is affected most by the new effects. Furthermore, using the world average branching ratio for the exclusive B decays at the 2σ level, we discuss the allowed values for the new parameters. Finally, we point out that the influence of the new physics effects on the direct CP asymmetry in B decays is insignificant.