Recently, HESS and other air Cerenkov telescopes have detected a source of TeV gamma -rays coincident with the Galactic center. It is not yet clear whether the gamma -rays are produced via leptonic or hadronic processes, so it is important to consider possible acceleration sites for the charged particles which produce the gamma -rays. One exciting possibility for the origin of these particles is the central black hole, Sgr A*, where the turbulent magnetic fields close to the event horizon can accelerate protons to TeV energies. Using a realistic model of the density distribution in a 6 pc*6 pc*6 pc cube at the Galactic center, we here calculate the trajectories followed by these TeV protons as they gyrate through the turbulent medium surrounding Sgr A*. Diffusing out from the black hole, the protons produce TeV gamma -rays via \pi0 decay following a collision with a proton in the surrounding medium. After following over 222,000 such trajectories, we find that the circumnuclear ring around Sgr A* can reproduce the observed 0.1-100 TeV HESS spectrum and flux if the protons are injected into this medium with an effective power-law index 0.75, significantly harder than the observed photon index of 2.25. The total energy in the steady-state 1-40 TeV proton population surrounding Sgr A* is inferred to be 2* 1047 ergs. Only 31% of the emitted 1-100 TeV protons encounter the circumnuclear torus, leaving a large flux of protons that diffuse outward to contribute to the Galactic ridge emission observed by HESS on scales of > 1^o.