Electron beam loss due to intra-beam scattering, the Touschek effect, in a storage ring depends on the electron beam polarization. The polarization of an electron beam can be determined from the difference in the Touschek lifetime compared with an unpolarized beam. In this paper, we report on a systematic experimental procedure recently developed at Duke FEL laboratory to study the radiative polarization of a stored electron beam. Using this technique, we have successfully observed the radiative polarization build-up of an electron beam in the Duke storage ring, and determined the equilibrium degree of polarization and the time constant of the polarization build-up process. Show Partial Abstract