The SciBooNE Collaboration reports K+ production cross section and rate measurements using high energy daughter muon neutrino scattering data off the SciBar polystyrene (C8H8) target in the SciBooNE detector. The K+ 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 d2{sigma}/dpd{Omega} = (5.34 times 0.76) mb/(GeV/c times sr) for p + Be -> K+ + X at mean K+ energy of 3.9 GeV and angle (with respect to the proton beam direction) of 3.7 degrees, corresponding to the selected K+ sample. Compared to Monte Carlo predictions using previous higher energy K+ production measurements, this measurement, which uses the NUANCE neutrino interaction generator, is consistent with a normalization factor of 0.85times0.12. This agreement is evidence that the extrapolation of the higher energy K+ measurements to an 8 GeV beam energy using Feynman scaling is valid. This measurement reduces the error on the K+ production cross section from 40% to 14%.