<p>The article investigates the frequency shifting of a laser carrying orbital angular momentum (OAM) in a cold collisionless plasma under the impact of a static magnetic field applied in the axial direction. Spatio-temporal variation of the laser intensity profile is investigated considering relativistic mass increase of the plasma electrons. Nonlinear Schrodinger equation is derived using Wentzel -Kramers - Brillouin (WKB) method and slowly varying envelope approximation. The frequency shifting is then discussed in connection with the spatio-temporal variation of the laser intensity. The effects of magnetic field along with the effects of the polarization states are discussed in detail. The relativistic frequency shifting is observed to enhance both rear side and front side of the pulse with the applied magnetic field. It is also observed that right circularly polarized (RCP) lasers undergo stronger shifting than the left circularly polarized (LCP) lasers. The results obtained in this article may find application in twisted harmonic generation, particle acceleration, optical manipulation and so on.</p>