  We address the description of a graphene Corbino disk in the context of a
tight binding approach that includes both kinetic and Rashba spin-orbit
coupling due to an external out-of-plane electric field. Persistent equilibrium
currents are induced by an external magnetic field breaking time reversal
symmetry. By direct diagonalization, we compute the spectrum and focus on the
dispersion near the $K$ points at the Fermi level. The dispersion keenly
reproduces that of a continuum model in spite of the complexity of the boundary
conditions. We validate the assumptions of the continuum model in terms of
predominant zig-zag boundaries conditions and weak sub-band coupling. The wave
functions displaying the lowest transverse modes are obtained, showing the
predominance of edge states with charge density at the zig-zag edges. The
persistent charge currents, nevertheless, do not follow the traditional
argument of current cancellation from levels below the Fermi level, and thus
they depart in the tight-binding from those found in the continuum model.
