Cementitious materials can capture CO2 through carbonation reaction during their service life and post-demolition. Indeed, construction and demolition waste (CDW) still have some potential for carbonation as they contain concrete and cement-based mortars. This research consists of an experimental programme to evaluate the CO2 capture of recycling aggregates (RAs) from CDW. Two types of CDW were studied, namely mixed recycled aggregates (MRAs) and recycled concrete aggregates (RCAs). The recycled aggregates were submitted to forced and accelerated carbonation at 23 °C, 60% relative humidity and 25% of CO2 concentration. This study contributes to the existing literature by investigating more realistic RA sources that have already absorbed atmospheric CO2 during their service life. From the experimental campaign, the results show that RCAs have higher carbonation potential when compared to MRAs due to the higher cementitious material content (Rc) and to the degree of natural carbonation. The recycled aggregates’ maximum CO2 capture was assessed by thermogravimetric analysis (TGA) at different CO2 exposure times. It was verified that the maximum CO2 capture, respectively, for MRAs and RCAs, occurred after 5 h and 12 h of exposition. In short, CDW captured from 5 wt.% to 35 wt.% of CO2 per tonne of cement paste, which corresponds to 0.6% to 4.1% per tonne of aggregate. It was concluded that the carbonation process of CDW has the potential to sequester from 123 kg to 225 kg of CO2 per tonne of cement paste for MRAs and 52 up to 491 kg of CO2 per tonne of cement paste for RCAs.