Raman backscattering is a parametric instability where an electromagnetic wave scatters from an electron plasma wave. The backscattered waves are downshifted by the plasma frequency where a linear frequency-matching relation exists. When laser intensity is sufficiently high, the linear frequency-matching relation is no longer valid and a frequency shift occurs in the spectrum of scattered waves. The present article is devoted to the investigation of the frequency shift of Raman backscattering in magnetized plasma for the first time. Plasma can either be magnetized due to the external magnetic field or the self-generated dc magnetic field. The orientation of magnetic field is assumed to be parallel to the laser wave vector. Insertion of perturbed current density leads to the derivation of the dispersion relation of circularly polarized waves through plasma fluid model. Solution of the dispersion relation leads to an analytic relation for the frequency shift of scattered waves. This frequency shift depends on plasma density, laser intensity and its polarization. Plots of the wavelength of scattered waves versus laser intensity show that the rise in laser intensity increases the wavelength of scattered waves. The increase is more pronounced in right-handed circularly polarized lasers. The rise in magnetic field magnitude increases the wavelength of right-handed circularly polarized scattered waves while it reduces the wavelength of its left-handed counterpart. Furthermore, the increase of plasma density increases the wavelength of scattered waves. This effect can provide a diagnostic tool for laser-plasma interactions.