X-ray photoelectron diffraction has been used to determine the molecular orientation of C-60 adsorbed as a monolayer on the Ag(001) surface. From an extended comparison to single scattering cluster calculations, we find the presence of two inequivalent prevailing molecular orientations of the C-60 cage, as well as a considerable fraction of rotationally not-ordered molecules. In this system, scanning tunneling microscopy (STM) investigations have shown the presence of two differently imaged molecules that the authors proposed to originate from different bonding states [E. Giudice et al, Surf. Sci. 405, L561 (1998)]. Our analysis suggests a relation between imaging property and rotational order or not-order, while the two prevailing orientations are not distinguished by the existing STM data in this case.