The 21Na(p,gamma)22Mg reaction is expected to play an important role in the nucleosynthesis of 22Na in oxygen-neon novae. The decay of 22Na leads to the emission of a characteristic 1.275 MeV gamma-ray line. This report provides the first direct measurement of the rate of this reaction using a radioactive 21Na beam, and discusses its astrophysical implications. The energy of the important state was measured to be E(c.m.)=205.7+/-0.5 keV with a resonance strength omegagamma=1.03+/-0.16(stat)+/-0.14(sys) meV.