The SciBooNE Collaboration reports K þ production cross section and rate measurements using highenergy daughter muon neutrino scattering data off the SciBar polystyrene (C 8 H 8 ) target in the SciBooNE detector. The K þ mesons are produced by 8 GeV protons striking a beryllium target in Fermilab Booster Neutrino Beam line (BNB). Using observed neutrino and antineutrino events in SciBooNE, we measure d 2 dpd ¼ ð5:34 AE 0:76Þ mb=ðGeV=c  srÞ for p þ Be ! K þ þ X at mean K þ energy of 3.9 GeV and angle (with respect to the proton beam direction) of 3.7 degrees, corresponding to the selected K þ sample. Compared to Monte Carlo predictions using previous higher energy K þ production measurements, this measurement, which uses the NUANCE neutrino interaction generator, is consistent with a normalization factor of 0:85 AE 0:12. This agreement is evidence that the extrapolation of the higher energy K þ measurements to an 8 GeV beam energy using Feynman scaling is valid. This measurement reduces the error on the K þ production cross section from 40% to 14%.