Small-angle neutron scattering experiments have been performed to investigate orientational ordering of a dispersion of rod-shaped ferromagnetic nanoparticles under the influence of shear flow and static magnetic field. In this experiment, the flow and flow gradient directions are perpendicular to the direction of the applied magnetic field. The scattering intensity is isotropic in zero-shear-rate or zero-applied-field conditions, indicating that the particles are randomly oriented. Anisotropic scattering is observed both in a shear flow and in a static magnetic field, showing that both flow and field induce orientational order in the dispersion. The anisotropy increases with the increase of field and with the increase of shear rate. Three states of order have been observed with the application of both shear flow and magnetic field. At low shear rates, the particles are aligned in the field direction. When increasing shear rate is applied, the particles revert to random orientations at a characteristic shear rate that depends on the strength of the applied magnetic field. Above the characteristic shear rate, the particles align along the flow direction. The experimental results agree qualitatively with the predictions of a mean field model.