The mechanical and chemical properties of plant cell walls greatly rely on the supramolecular assembly of cellulose fibrils. To study the local orientation of cellulose in secondary plant cell walls, diffraction limited infrared (IR) micro-spectroscopic mapping experiments were conducted at different orientation of transverse leaf section of the grass Sorghum bicolor with respect to the polarization direction of the IR radiation. Two-dimensional maps, based on polarization-sensitive absorption bands of cellulose were obtained for different polarization angles. They reveal a significant degree of anisotropy of the cellulose macromolecules as well as of other biopolymers in sclerenchyma and xylem regions of the cross section. Quantification of the signals assigned to polarization sensitive vibrational modes allowed to determine the preferential orientation of the sub-micron cellulose fibrils in single cell walls. A sample of crystalline nano-cellulose comprising both a single microcrystal as well as unordered layers of nanocrystals was used for validation of the approach. The results demonstrate that diffraction limited IR micro-spectroscopy can be used to study hierarchically structured materials with complex anisotropic behavior.