Properties of recycled aggregate concrete (RAC) are influenced by the composition and particle size distribution of recycled coarse aggregate (RCA). The study herein designed seven distinct groups of RACs with varying aggregate fractal dimensions (D) and one group of natural concrete (NAC). The impact of D on the workability, compressive strength, resistance to chloride ion penetration, and carbonation resistance of RAC was measured. It was found that an increase in the D value led to a decrease in the slump and slump flow, with the compressive strength and chloride ion penetration increasing and then decreasing, and carbonation gradually declined. The optimal fractal dimension was thereby determined to be 2.547 by a strength model accommodating two parameters of D and the curing age. Additionally, the mass percentage of each particle size for the corresponding gradation was presented. The compressive strength and chloride permeation resistance of RAC (D = 1.0) relative to RAC (D = 2.5) was increased by 16.7% and 13.3%, respectively. Furthermore, the carbonation depth of RAC (D = 2.5) was comparable to that of NAC. Additionally, the carbonation resistance of RAC was influenced by both the size distribution and the degree of natural carbonation of RCA, resulting in four distinct features relative to NAC. It is thereby feasible to enhance RAC performance through the manipulation of RCA’s fractal dimensions.