We have performed the first direct measurement of the ^{38}K(p,γ)^{39}Ca reaction using a beam of radioactive ^{38}K. A proposed ℓ=0 resonance in the ^{38}K+p system has been identified at 679(2) keV with an associated strength of 120_{-30}^{+50} meV. Upper limits of 1.16 (3.5) and 8.6 (26) meV at the 68% (95%) confidence level were also established for two further expected ℓ=0 resonances at 386 and 515 keV, respectively. The present results have reduced uncertainties in the ^{38}K(p,γ)^{39}Ca reaction rate at temperatures of 0.4 GK by more than 2 orders of magnitude and indicate that Ar and Ca may be ejected in observable quantities by oxygen-neon novae. However, based on the newly evaluated rate, the ^{38}K(p,γ)^{39}Ca path is unlikely to be responsible for the production of Ar and Ca in significantly enhanced quantities relative to solar abundances.