The large and reversible photoinduced linear and circular birefringences in azo-compounds are at the basis of the interest in these materials, which are potentially useful for several applications. Since the onset of the linear and circular anisotropies relies on orientational processes, which typically occur on the molecular and supramolecular length scale, respectively, a circular birefringence at least one order of magnitude lower than the linear one is usually observed. Here, the synthesis and characterization of an amorphous polymer with a dimeric repeating unit containing a cyanoazobenzene and a cyanobiphenyl moiety are reported, in which identical optical linear and circular birefringences are induced for proper light dose and ellipticity. A pump-probe technique and an analytical method based on the Stokes-Mueller formalism are used to investigate the photoinduced effects and to evaluate the anisotropies. The peculiar photoresponse of the polymer makes it a good candidate for applications in smart functional devices.