The Mg-24(p,alpha)Na-21 reaction was measured at the Holifield Radioactive Ion Beam Facility of the Oak Ridge National Laboratory to study the spectroscopy of the radionuclide Na-21. A 31-MeV proton beam from the 25 MV tandem accelerator bombarded isotopically enriched Mg-24 targets. Recoiling He-4 particles were identified by an annular silicon strip detector array. Two energy levels at E-x = 6.594 and 7.132 MeV were observed for the first time. By comparing the experimentally obtained angular distributions and distorted wave Born approximation calculations, the spins and parities of Na-21 energy levels were constrained. The astrophysicallyi-mportant F-17(alpha, p)Ne-20 reaction rate was also calculated for the first time using resonance parameters for 12 energy levels.