The knowledge of the turbulence characteristics is a key point to build models able to predict the confinement time in a fusion reactor. A method to extract the radial profile of the density fluctuations from the fast swept reflectometry phase signal is proposed and tested on Tore Supra (TS). The relationship between the wavenumber spectrum of the set of phase perturbations obtained during a frequency sweep and the wavenumber spectrum of the turbulence itself is the aim of the method. This relationship can be derived analytically for the O-mode. For the X-mode it is established by full wave simulations. As a result, the radial profile of density fluctuations can be obtained from a mere integration of the wavenumber spectrum of the phase fluctuations. The assumptions used to establish this diagnostics and its limitations are discussed by using simulations. Then the method is applied to recover the radial profile of the density fluctuations in the cases of the TS fast swept reflectometer data. With this method, the expected density profile evolution as a function of the plasma current is clearly shown.