  We address the problem of persistent charge and spin currents on a Corbino
disk built from a graphene sheet. We consistently derive the Hamiltonian
including kinetic, intrinsic (ISO) and Rashba spin-orbit interactions in
cylindrical coordinates. The Hamiltonian is carefully considered to reflect
hermiticity and covariance. We compute the energy spectrum and the
corresponding eigenfunctions separately for the intrinsic and Rashba spin-orbit
interactions. In order to determine the charge persistent currents we use the
spectrum equilibrium linear response definition. We also determine the spin and
pseudo spin polarizations associated with such equilibrium currents. For the
intrinsic case one can also compute the correct currents by applying the bare
velocity operator to the ISO wavefunctions or alternatively the ISO group
velocity operator to the free wavefunctions. Charge currents for both SO
couplings are maximal in the vicinity of half integer flux quanta. Such maximal
currents are protected from thermal effects because contributing levels plunge
($\sim$1K) into the Fermi sea at half integer flux values. Such a mechanism,
makes them observable at readily accessible temperatures. Spin currents only
arise for the Rashba coupling, due to the spin symmetry of the ISO spectrum.
For the Rashba coupling, spin currents are cancelled at half integer fluxes but
they remain finite in the vicinity, and the same scenario above protects spin
currents.
