We design a circularly polarized laser pulse in the infrared frequency and femtosecond time domains, for excitation of the OsH(4) molecule in its first excited pseudorotational state of the triply-degenerate bend. The OsH(4) molecule need not be pre-oriented. After excitation, the central nucleus Os carries out pseudorotation about the axis parallel to the direction of propagation of the laser pulse. This pseudorotation causes a strong electric ring current with a value I=1.53 e fs(-1). The mean value of the radius of the ring current is very small, R=0.0031 a(0), where a(0) is the Bohr radius. According to the Biot-Savart law (|B(R=0)| ~I/R)), this nuclear ring current induces the strongest magnetic field predicted so far in molecules, with a central peak absolute value |B(R=0)| =623 T. To monitor the effect, we propose an IR-pump-X-ray-probe versus an X-ray-probe-only experiment, at the K- and L-edges of X-ray ionization. The results are based on the general quantum theory of excitations of pseudorotations in tetrahedral molecules AB(4), driven by a circularly polarized laser pulse.