Polarization selective devices, such as polarizers and polarization selective resonant cavities (e.g., gratings and ring resonators), are core components for polarization control in optical systems and find wide applications in polarization-division-multiplexing, coherent optical detection, photography, liquid crystal display, and optical sensing. In this paper, we demonstrate integrated waveguide polarizers and polarization-selective micro-ring resonators (MRRs) incorporated with graphene oxide (GO). We achieve highly precise control of the placement, thickness, and length of the GO films coated on integrated photonic devices by using a solution-based, transfer-free, and layer-by-layer GO coating method followed by photolithography and lift-off processes. The latter overcomes the layer transfer fabrication limitations of 2D materials and represent a significant advance towards manufacturing integrated photonic devices incorporated with 2D materials. We measure the performance of the waveguide polarizer for different GO film thicknesses and lengths versus polarization, wavelength, and power, achieving a very high polarization dependent loss (PDL) of ~ 53.8 dB. For GO-coated integrated MRRs, we achieve an 8.3-dB polarization extinction ratio between the TE and TM resonances, with the extracted propagation loss showing good agreement with the waveguide results. Furthermore, we present layer-by-layer characterization of the linear optical properties of 2D layered GO films, including detailed measurements that conclusively determine the material loss anisotropy of the GO films as well as the relative contribution of film loss anisotropy versus polarization-dependent mode overlap, to the device performance. These results offer interesting physical insights and trends of the layered GO films from monolayer to quasi bulk like behavior and confirm the high-performance of integrated polarization selective devices incorporated with GO films.