Cosmic ray access to Jupiter's magnetosphere is investigated by numerical calculations of cosmic ray trajectories in the combined magnetic fields of the planetary dipole and the magnetospheric current sheet. Entry along the current sheet allows cosmic rays to reach closer to Jupiter than they would in a dipole planetary magnetic field alone. Observations of galactic cosmic rays from Galileo show that the calculations underestimate the true cutoff rigidities at equatorial radial distances >10 RJ, but that the calculated ~14 GV cutoff rigidity at 10 RJ is a reasonable estimate.