  The effect of spin-orbit interaction on persistent currents in mesoscopic
Hubbard rings threaded by an Aharonov-Bohm flux is investigated putting stress
on the orbital magnetism. The non-perturbative treatment of the spin-orbit
interaction developed by Meir {\em et al.} is combined with the Bethe ansatz
solution to deal with this problem exactly. We find that the interplay of
spin-orbit interaction and electron-electron interaction plays a crucial role,
bringing about some new effects on the orbital magnetism.
