This study is to be seen in the context of the replacement of oil-based polymers by new bio- sourced ones having the same end-user properties. It is also important to use green chemical engineering to process them in a more environmental friendly way. The use of supercritical fluids appears then, to be a promising route. The most interesting fluid is supercritical carbon dioxide (sc-CO2), which is soluble in quite significant quantities in many molten polymers, where it acts as a plasticizer and a swelling agent. It is known to be a green processing agent used, for instance, such as blending of polymers, polymer foaming, particle formation or polymerisation process. The easiest and most used way of processing polymers in continuous mode is to use an extruder that provides a high shear rate, particularly in the die. Our lab has developed a process coupling single-screw extrusion and sc-CO2. Understanding and improving such process require data, like the solubility of CO2 into the polymer, the diffusion coefficient and the viscosity of the mix. We have then developed an on-line measurement of the viscosity based on capillary rheometry. The method was validated by measurements on a classic capillary rheometer. Both data sets were found in good agreement. This method was applied to characterize the rheology of a bio-sourced polymer (BsP) itself and of the polymer-CO2 binary system. A pseudoplastic fluid behaviour was observed with a 30 % decrease of the viscosity from 46 to 32 Pa.s at about 5000 s-1 and 220°C, upon addition of carbon dioxide. The rheological data were correlated with solubility data and analysed in function of the process parameters. It was observed that the decrease of the viscosity with the amount of CO2 dropped to a plateau before reaching the thermodynamic solubility. It seems that the limitations are due to the kinetics of dissolution and mixing. The higher the shear stress, the higher the amount of CO2 at which the viscosity plateau is reached. This is an indication of a better CO2 dissolution rate when the speed of the screw increases. Therefore, those measurements may quantify the impact of the CO2 on the rheology of the system but also of the efficiency of the mixing process in our experimental setup.