Using linearly polarized X-rays for investigations on noncrystalline samples, information on the orientation of the investigated local structure with respect to a nanostructure (e.g., membranes, proteins. layered compounds, and polymers) or a textured macroscopic structure (e.g., a rough surface) may become accessible in case the considered molecular system is partially ordered. For systems with a preferential orientation of ons axis of the molecular coordinate system (M, e.g., the membrane normal) with respect to a vector in the macroscopic sample system (S, typically the normal to the macroscopic sample surface), an equation is derived which describes the dependence of the EXAFS on (i) theta(E), the angle between the X-ray electric field vector and S, (ii) a single order parameter, (iii) theta(R), the angle between the absorber-backscatterer vector and M. A data-evaluation method is proposed which involves a joint-fit of EXAFS spectra measured for, at least, two excitation angles, theta(E). Our approach accounts correctly for partial disorder; and it allows an exact single-scattering, curved-wave treatment of the EXAFS originating from an absorber-backscatterer pair of unknown orientation. An approximative and the curved-wave approach for evaluation of EXAFS dichroism data are compared.