All-loop asymptotic Bethe equations for a 3-parameter deformation of AdS5/CFT4 have been proposed by Beisert and Roiban. We propose a Drinfeld-Reshetikhin twist of the AdS5/CFT4 S-matrix, together with c-number diagonal twists of the boundary conditions, from which we derive these Bethe equations. On the other hand, certain twists of the S-matrix elements describe the ?-deformation of $N = 4$ supersymmetric Yang-Mills theory. We computed the perturbative four-loop anomalous dimension of one-impurity states and the Konishi operator of the deformed gauge theory from the Luescher formula based on these twisted S-matrix elements. The result agrees exactly with the perturbative gauge theory computations.