Polarization of starlight may arise from absorption and scattering by elongated dust grains that are at least partially aligned by a magnetic field. We assume that the grains contain mostly compounds of hydrogen with about 12 per cent iron by weight, presumably also in compounds. The theory of Gans is used to compute the scattering and absorption by a spheroidal grain small compared to the wave length, the component of the light with its electric vector parallel to the grain's long axis being preferentially weakened. The polarization and extinction of light are then computed for a cloud of small patticles (mean radius 10- X 10-i cm) having any specified distribution of orientations. Our mechanism for orienting the rapidly spinning grains (angnlar velocities of the order of rad/sec) is the small nonconservative torque due to paramagnetic relaxation in material containing a few per cent of iron. The magnitude of the paramagnetic absorption is estimated from theory and experiment. This torque tends to make the short axis of the grain the axis of rotation, which is still very rapid, and to set this short axis along the magnetic field (orientation rate of the order of 10- 10-ii rad/sec). Thus the maximum extinction coefficient is for light with its electric vector perpendicular to the field. An approximate statistical theory based on a relaxation time (of the order of 10i3 sec) for the orientation of the grains gives the distribution of orientations to be expected when this tendency toward orientation is balanced by the tendency toward random alignment caused by the bombardment of the grains by the interstellar gas. Small prolate grains of eccentricity such that the ratio of diameters lies in the range 1.2-1.7 will be sufficiently aligned to produce the observed ratio of polarization to color excess, P/Ei < 0.18, in a magnetic field of 10- 1(h gauss. The theory predicts that for uniform magnetic fields and interstellar matter of constant temperature and composition the polarization should be proportional to the color excess. The direction of the observed polarization vectors indicates that over regions of several hundred parsecs in the Milky Way the magnetic field is mainly parallel to the plane of the galaxy, perhaps nearly uniform along a spiral arm or perhaps making random whirls mainly in the plane of the galaxy. Since the interstellar grains are larger than those to which the Gans theory applies and since the predicted wave-length dependence of the extinction is incorrect, it is not surprising that the theory gives an incorrect wave-length dependence of the polarization. Qualitative considerations indicate that the predicted ratio p/Ei is not too far from the correct order of magnitude and that present observations of the wave4ength dependence do not necessarily contradict the rest of our theory, which can be extended when extinction coefficients are known for large grains. Observational data are summarized in § 1, and the nature of the grains is treated in § 4; our theory is given in outline in § 3, and the mathematical details are worked out in §§ 5-7. In § 8 we show that torques due to eddy currents or to static charges on the grain are unimportant.