Complex fiber composites such as biological materials frequently exhibit local fiber textures which can be determined quantitatively by scanning X-ray microdiffraction techniques. The experimental necessity of keeping the illuminated diffraction volume fixed usually leads to complex diffraction patterns, depending on the orientation of the fiber axis with respect to the direction of the primary X-ray beam. Here, an analytical expression is derived that relates the azimuthal intensity distribution measured with an area detector to the orientation distribution of the fibers within the specimen. The validity of the relation is demonstrated for a single flax fiber, which was investigated by microbeam X-ray diffraction using synchrotron radiation.