Possible experiments on the observation of the P,T - odd Faraday effect (rotation of polarization plane for the light, propagating through a medium in the presence of an external electric field, P - is the space inversion, T - is the time reflection) caused by the electron electric dipole moment in atoms and molecules, are discussed theoretically. An observation is assumed to be performed on the basis of modern intra-cavity absorption spectroscopy (ICAS) combined with atomic (molecular) beam techniques. The P,T - odd optical rotation is due to the linear Stark splitting of atomic or molecular levels. This leads to the difference between the refractive indexes for the right and left circularly polarized photons.