Polyethylene terephthalate (PET) plastic-waste-derived activated carbons have recently been developed and exhibit excellent CO2 adsorption uptake. However, the CO2-adsorption performance of such recycled materials has only been considered on a basic characterization level and has not yet been evaluated in carbon capture cycles, thereby making biased analyses inevitable. Consequently, a whole chain including the material, process, and cycle is essential for comprehensively analyzing and evaluating novel CO2 adsorbents. Therefore, in this study, various CO2-capture cycles using PET plastic-waste-derived activated carbon adsorbents were numerically simulated, the cyclic CO2-adsorption performances were evaluated, and the application scenario was optimized. A methodology for evaluating the cyclic CO2-adsorption performance of PET plastic-waste-derived activated carbon was proposed for CO2 capture. The results suggested that the temperature/vacuum swing adsorption cycle was superior and that its maximum exergy efficiency reached 32.90%.