The aim of this study is to investigate the feasibility of recycling the recycled plastic-modified asphaltic mixtures, particularly for surface course of road pavements and to examine its performance properties as well as the environmental impact with respect to water leachability. Three types of recycled plastic wastes, namely polypropylene (PP), polyethylene (PET), and polystyrene (PS) were used in the study. The recycled plastic-modified samples were prepared using dry mixing method and artificially aged in the oven following AASHTO R30 method to simulate 5–7 years of aging in the field. A series of laboratory tests such as Marshall stability, Indirect tensile strength, Cantabro abrasion loss, and resilient modulus tests were performed to evaluate the performance of recycled asphalt concrete containing 20% aged content. The results demonstrate that the recycled mix of plastic-modified recycled asphalt concrete performed better than the conventional mix in terms of metrics considered in our experiments. In terms of the environmental impact study, the results of the water leachability tests indicated that the recycled mix with inclusion of recycled plastic containing 20% aged content had an insignificant influence on the leachability of water contaminants. The findings suggest that the use of recycled mix containing waste plastic in asphalt mixes has the potential to contribute to reduced environmental impact and promote sustainable practices in the construction industry.