Recycled aggregate (RA) made from waste concrete has inferior fundamental properties, i.e., apparent density, water absorption, mass variation, carbonation ratio, etc., compared to those of natural aggregate (NA), severely restricting its application in practical projects. However, using CO2 to accelerate RA carbonation can effectively improve these properties, and this treatment approach can promote energy savings and sustainable development. The accelerated carbonation curing conditions for RA can significantly impact the modification effect of RA. For this purpose, this paper used recycled coarse aggregate (RCA) as a case study. An accelerated carbonation modification treatment experiment for RCA under different accelerated carbonation curing conditions was carried out, and the effects of relative humidity and CO2 concentration on the apparent density, water absorption, moisture content, mass variation and carbonation ratio of RCA under a constant ambient temperature were explored and quantified. The results indicated that the best-accelerated carbonation curing conditions applicable to this paper’s RCA were confirmed as being an environmental temperature of 20 °C and a relative humidity of 70%, as well as a CO2 concentration of 20%. Under these conditions, the apparent density and water absorption of CRCA are approximately 1.04 times and 75.30% higher than those of RCA, and, in addition, the carbonation ratio for RCA under the optimal accelerated carbonation curing conditions is all higher than others, thus improving the properties of RCA to a certain degree. Finally, in this paper, the variation trends of the RCA property indexes in terms of carbonation time treated by the best accelerated carbonation curing conditions are examined, and the time-varying models for the RCA property indexes during the accelerated carbonation are established.