We present Atacama Large Millimeter/submillimeter Array CO (J = 2-1) and 1.3 mm continuum observations of the high-velocity jet associated with the FIR 6b protostar located in the Orion Molecular Cloud-2. We detect a velocity gradient along the short axis of the jet in both the red- and blueshifted components. The position-velocity diagrams along the short axis of the redshifted jet show a typical characteristic of a rotating cylinder. We attribute the velocity gradient in the redshifted component to rotation of the jet. The rotation velocity (>20 km s(-1)) and specific angular momentum (>10(22) cm(2) s(-1)) of the jet around FIR 6b are the largest among all jets in which rotation has been observed. By combining disk wind theory with our observations, the jet launching radius is estimated to be in the range of 2.18-2.96 au. The rapid rotation, large specific angular momentum, and a launching radius far from the central protostar can be explained by a magnetohydrodynamic disk wind that contributes to the angular momentum transfer in the late stages of protostellar accretion.