It is predicted that oriented BeO molecules would give rise to unprecedentedly strong, unidirectional electric ring current and an associated magnetic field upon excitation by a right or left circularly polarized laser pulse into the first excited degenerate singlet state. The strong toroidal electric ring current of this state is dominated by the ring current of the 1pi(+/-) orbital about the molecular axis. Our predictions are based on the analysis of the orbital composition of the states involved and are substantiated by high level electronic structure calculations and wavepacket simulations of the laser-driven orientation and excitation dynamics.