We study the effect of rotational state-dependent alignment in the scattering of molecules by optical fields. CS2 molecules in their lowest few rotational states are adiabatically aligned and transversely accelerated by a nonresonant optical standing wave. The state-dependent alignment in the standing wave has a significant effect on the molecular acceleration that occurs in the steep field gradient of the standing wave potential. This effect is strong at low rotational temperatures of the molecules. Dramatic changes of measured velocity distribution caused by the optical standing wave are well reproduced by numerical simulations based on the rotational-state-dependent alignment but cannot be modeled when ignoring these effects. Moreover, the molecular scattering by an off-resonant optical field amounts to manipulating the translational motion of molecules in a rotational-state-specific way. Conversely, our results demonstrate that scattering from a nonresonant optical standing wave is a viable method for rotational state selection of non-polar molecules.