We present a measurement of RB, the ratio of the branching fraction for the rare decay D0→K+π− to that for the Cabibbo-favored decay D0→K−π+. Charge-conjugate decays are implicitly included. A signal of 2005±104 events for the decay D0→K+π− is obtained using the CDF II detector at the Fermilab Tevatron collider. The data set corresponds to an integrated luminosity of 0.35  fb−1 produced in pp collisions at s√=1.96  TeV. Assuming no mixing, we find RB=[4.05±0.21(stat)±0.11(syst)]×10−3. This measurement is consistent with the world average, and comparable in accuracy with the best measurements from other experiments.