In this article, we present the influence of structured light on the line shape of closed hyperfine transition F = 2 → F′ = 3 of 87Rb-D2 line by monitoring the linearly polarized probe Gaussian beam in the presence of circularly polarized pump Laguerre-Gaussian (LG) beam having different orders of orbital angular momentum (OAM). It is observed that both the amplitude and line-width of the closed hyperfine signal under polarization spectroscopy (PS) are enhanced (reduced) with the increasing values of the pump light ellipticity for the non-zero-order (zero-order) OAM. Furthermore, the dispersion-like PS signal of the closed hyperfine transition is modified by varying the pump power and angular mismatch of the pump-probe beams. The experimental results demonstrate that the anisotropy of an atomic medium can be influenced by the OAM of light and can be further modulated by tuning the ellipticity of the structured light.