Powder samples can show pronounced texture effects in X-ray scattering. Here, texture effects are described theoretically for circularly ordered fibers and shown experimentally for a special type of these fibers based on nanostructured silica. The systematic diffraction peak intensity dependences, observed with the tilting of the samples, fit well with the theoretical model proposed and can be used as an efficient detection method for circulite-type mesopore organization. Our investigations clearly emphasize the difficulties encountered in the interpretation of peak intensities in the X-ray scattering analyses because of pronounced texture effects.