We present measurements of the B+ meson total cross section and differential cross section dσ/dpT. The measurements use a 98±4 pb-1 sample of pp¯ collisions at s√=1.8 TeV collected by the CDF detector. Charged B meson candidates are reconstructed through the decay B±→J/ψK± with J/ψ⃗ μ+μ-. The total cross section, measured in the central rapidity region |y|<1.0 for pT(B)>6.0 GeV/c, is 3.6±0.6(stat⊕ syst) μb. The measured differential cross section is substantially larger than typical QCD predictions calculated to next-to-leading order.