When light interacts with matter, dichroism with respect to the handedness of circularly polarized light is well established. But what happens if the light further possesses an orbital angular momentum? In this paper, we discuss possible definitions of orbital angular momentum dichroism and define a new type of dichroism, the class dichroism. By numerically calculating the scattering cross-section spectra, we study the dichroism of a plasmonic nanostructure interacting with orbital angular momentum light. By considering the exemplary case of twisted, stacked nanorods, we show that the orbital angular momentum dichroism can be as strong as dichroism induced by circular polarization. We present a detailed classification of the different types of orbital angular momentum dichroism, which paves the way for new chiroptic spectroscopic techniques.