Radiative torques on irregular dust grains, in addition to producing superthermal rotation, play a direct dynamical role in the alignment of interstellar dust with the local magnetic field. The equations governing the orientation of spinning, precessing grains are derived; H₂ formation torques and paramagnetic dissipation are included in the dynamics. Stationary solutions (constant alignment angle and spin rate) are found; these solutions may be stable ("attractors") or unstable ("repellors"). The equations of motion are numerically integrated for three exemplary irregular grain geometries, exposed to anisotropic radiation with the spectrum of interstellar starlight. The resulting "trajectory maps" are classified as "noncyclic," "semicyclic," or "cyclic," with examples of each given.

We find that radiative torques result in rapid grain alignment, even in the absence of paramagnetic dissipation. It appears that radiative torques due to starlight can account for the observed alignment of interstellar grains with the Galactic magnetic field.