28 pages, 3 tables, 10 figures Submitted to Phys. Rev. D ; We present a new measurement of the $B^+$ meson differential cross section $dσ/d p_T$ at $\sqrt{s}=1960$ GeV. The data correspond to an integrated luminosity of 739pb$^{-1}$ collected with the upgraded CDF detector (CDF II) at the Fermilab Tevatron collider. $B^+$ candidates are reconstructed through the decay $B^+ \to J/ψ K^+$, with $J/ψ \to μ^+ μ^-$. The integrated cross section for producing $B^+$ mesons with $p_T ≥ 6$ GeV/c and $|y| ≤ 1$ is measured to be $2.78 ± 0.24 μ$b