An integral back-transform has been developed to retrieve the polar magnetic component in a cylindrically symmetric plasma from a single projection. The formula is derived from parallel forward Radon transform (Abel transform) of a source-free vector field. Two numerical schemes are proposed to solve the backward transform. These schemes have been tested successfully with predefined plasma parameters. The practical application to the analysis of experimental Faraday rotationmeasurements is also presented, leading to the reconstruction of the transverse profile of the magnetic field.