A 40-keV mass-separated radioactive beam of N-13(1+) ions has been polarized using the technique of grazing surface scattering (GSS) at a Si single crystal. A nuclear polarization of 11% was obtained. It was detected by measuring the beta asymmetry after implantation of the beam in a Pt foil at a temperature of 20 mK. This result demonstrates the feasibility of GSS as a general method for the production of polarized radioactive beams. The technique can be applied to low-intensity beams and used for investigations ranging from symmetry tests in weak interactions to solid-state studies.