We propose a density-functional theory (DFT) to describe inhomogeneous mixtures of AB random copolymer and carbon dioxide (CO2). The statistical sequence of monomer in the polymer chain backbone is modeled by a transition matrix in a Markov-step growth process. The parameters of the theory are determined by fitting the bulk experimental data. We apply the DFT to the interfacial properties of binary mixtures of CO2 with poly(methyl methacrylate co ethyl methacrylate) (P(MMA-co-EMA)), poly(methyl methacrylate co ethyl acrylate) (P(MMA-co-EM and poly(styrene co ethyl acrylate) (P(S-coEA)). The dependence of CO, solubility and interfacial tension on the copolymer composition and pressure is examined. We find that higher fractions of EA or EMA result in higher solubility of CO2 at a given pressure, but also results in higher interfacial tension at a fixed CO2 content in the polymer-rich phase. Using the classical nucleation theory as a rough estimate, we examine the effect of the copolymer composition on the free energy barrier of bubble nucleation in random copolymer-CO2 mixtures.