The electrical properties of a carbon nanotube depend strongly on its lattice structure as defined by chiral and translational vectors. A toroidal shape for a nanotube allows various twisted structures to exist along the direction of the tube axis. We theoretically investigate the kinematics of conducting electrons and persistent currents in toroidal carbon nanotubes. We show that persistent currents exhibit a special characteristic of the cylindrical lattice structure in twisted cases. We discuss the possibilities that the twist alters the period of the current to one half the flux quantum and that the current flows without an external magnetic field.