We propose a new density-functional theory (DFT) describing inhomogeneous polymer carbon dioxide (CO2) mixtures. The theory is constructed by combining the bulk Peng-Robinson equation of state (PR-EOS) with the statistical associating fluid theory (SAFT) and the fundamental measure theory (FMT). The weight density functions from FMT are used to extend the bulk excess Helmholtz free energy of PR-EOS to the inhomogeneous case, while the SAFT is used to describe correlations due to polymer chain connectivity and short-range forces due to weakly polar or association interactions. The additional long-range dispersion contributions are included using a mean-field approach. We apply our DFT to the interfacial properties of polystyrene-CO2 and poly(methyl methacrylate)-CO2 systems. The calculated interfacial tension values are in good agreement with experimental data at low to intermediate pressures. The inclusion of association energy for CO2 is shown to have a significant effect. We also point out the limitation of the PR-EOS for describing polymer-CO2 mixtures at high pressures (P > 35 MPa).