The Faraday effect should provide a direct method for the measurement of the current density profile in a tokamak fusion device. Measuring the angle of rotation of linearly polarized far‐infrared beams propagating along several vertical chords in the poloidal plane and then applying proper inversion techniques, will provide information about the current density profile. Assuming the Voigt effect is small, a solution is found using the WKB approximation. Due to the large Ohmic heating currents and plasma densities in Alcator C, sufficiently large angles of rotation are produced with a relatively short wavelength sufficient to make the Voigt and refractive effects negligible. For Alcator A the peak rotation is found to be the order of 4°, for Alcator C it is 12°. These values were calculated assuming a wavelength of 120 &mgr;m and ’’typical’’ plasma parameters. In Alcator C, in particular, the large rotation angles should allow measurement of the poloidal field over most of the plasma cross sections.