The high-resolution X-ray absorption spectra of rat tibia cortex have been measured for two different orientations of the bone long axis in respect to the electric field vector of linear polarized synchrotron radiation. Our measurements performed near the Ca 2p and O 1s absorption edges have revealed the substantial element-specific orientation dependence of the X-ray absorption coefficient. Strong changes in intensity of core-to-valence transitions are detected near the Ca L2,3 absorption edges, whereas minor changes occur near the O K absorption edge. The specific behavior is attributed to the emergent properties of X-ray linear dichroism in cortex. This optical phenomenon is assigned with relationship between the chemical Ca–O bonds in bone and hierarchical organization of the skeleton. The hierarchy-induced X-ray linear dichroism is discussed in the framework of the 3D superlattice model and Wolff paradigm. Prospects for using this phenomenon for medical diagnosis are also being discussed.