In this study, the simultaneous effect of recycled aggregates (recycled fine and coarse aggregates obtained from crushed waste concrete) and the potential improvement induced by acrylic polymer were investigated. First, concrete specimens containing different replacement levels of recycled fine and coarse aggregates (12.5%, 25%, 50%, and 100%) were examined separately. Subsequently, concrete mixes containing both fine and coarse recycled aggregates were tested. In the next stage, different contents of acrylic polymer (0.25%, 0.5%, 1%, 2%, 4%, and 8%) were incorporated to evaluate its influence on concrete performance. Finally, the synergistic effect of polymer and recycled aggregates on the mechanical behavior of concrete was assessed. For all mixtures, compressive strength was measured at curing ages of 7, 14, and 28 days. The results indicated that the use of recycled fine and coarse aggregates led to reductions in compressive strength by approximately 37% and 28%, respectively. The combined use of both recycled fine and coarse aggregates resulted in an even greater reduction in strength. However, the incorporation of polymer at its optimum content of 4% significantly enhanced the compressive strength across all mix designs. At this optimum level, a remarkable increase of 114% was observed compared to the control concrete. At a low dosage of 0.25%, the polymer effectively mitigated the detrimental effects of recycled aggregates. Furthermore, at 4% polymer content, the mechanical properties of concrete containing recycled fine, coarse, and combined aggregates increased by approximately 109%, 107%, and 100%, respectively, relative to the control specimen.