To demonstrate that measurements of X-ray linear dichroism are effective for determining bond orientations in disordered materials, we report the first observation of X-ray linear dichroism at the iodine L1-edge. The iodine-containing molecular solid studied in this work was the inclusion compound containing 4,4'-diiodobiphenyl guest molecules in the perhydrotriphenylene host structure. In this material, the guest substructure does not exhibit three-dimensional ordering, and thus diffraction-based techniques do not provide insights on the orientational properties of the guest molecules. Iodine L1-edge X-ray absorption spectra, recorded as a function of orientation of a single crystal of the material, exhibit significant dichroism (whereas no dichroism is observed at the iodine L2- and L3-edges). From quantitative analysis of the X-ray dichroism, the orientational properties of the C-I bonds within this material are established. The results pave the way for applying X-ray dichroism to determine molecular orientational properties of other materials, especially for partially ordered materials such as liquid crystals, confined liquids, and disordered crystalline phases, for which diffraction techniques may not be applicable.