It is shown that the current distribution in JET can be determined from the geometry of the flux surfaces inferred from surfaces of constant X-ray emissivity. Such surfaces, represented as shifted ellipses, are obtained from tomography of soft X-ray data. The relationship between the ellipticity and shift of the surfaces and the current distribution is found analytically. The current distribution is found to agree with that derived from full equilibrium calculations which use external magnetic data. An analysis of the sensitivity of the results to errors in the experimental data shows that the errors on the tomographic reconstruction need to the smaller than is currently feasible if the error on the axial safety factor is required to be below 10%.