Averaged equations describing the evolution of the orientation distribution in a dilute suspension of axisymmetric ‘‘tracer’’ particles flowing through a fixed bed of spheres or fibers are derived. The orientations of the freely suspended ‘‘tracer’’ particles change because of the stochastically fluctuating velocity field induced by the randomly distributed fixed‐bed particles. In the limit of small fixed‐bed volume fraction the orientation distribution satisfies a local orientational advective‐diffusion equation with an effective rotary diffusivity and ‘‘drift’’ velocity, which are functions of the orientation of the particle relative to the direction of the average flow. Solutions of this equation show that the tracer particles tend to align with their ‘‘thin side’’ toward the direction of the bulk flow and that the degree of this alignment depends on the aspect ratio of the particle.