We present a new magnetic field generation mechanism in underdense plasma due to plasma waves driven by co-propagating Laguerre-Gaussian (LG) beating orbital angular momentum (OAM) laser beams with both a different frequency and also different twist index.  In this plasma wave, particles oscillate elliptically in the transverse plane with an azimuthally dependent phase.    The distribution and evolution of density and electric field in the transverse plane has some special characteristics. We present a linear fluid model and also a high order analysis of the electrical current based on particle motion. To the second order, there is a net nonlinear rotating current leading to the onset of an intense axial magnetic field (up to 0.4 MG), which persists over a long time in the plasma (ps scale). It is different from Inverse Faraday effects. Our analytical predictions are confirmed in three-dimensional particle-in-cell simulations using EPOCH. This new method of magnetic field creation may find applications in charged beam collimation and controlled fusion.