In Mexico, approximately 6.5 million tons of plastic waste is generated, of which 38–58% is improperly managed and has the potential to leak into the environment. Furthermore, producing natural aggregates is associated with the unsustainable use of non-renewable resources. In this sense, this work aimed to evaluate the influence that recycled aggregates from plastic waste have on the behavior of concrete. Coarse aggregates of thermoplastic paint (TP) from paving waste were prepared and incorporated into four mixes, with concentrations of 5 to 20%. In addition, three mixes with fine aggregates from PET were evaluated as one reference mix. The studied properties were slump, compressive strength, flexural strength, rebound number, density, absorption, and porosity. The results indicate that both aggregates have significant potential for use in concrete, including structural use, when replacement percentages of around 5% are considered, with property losses not exceeding 8%. Their use is proposed for active mobility infrastructure, with percentages of up to 20% analyzed in this study. Finally, it is necessary to analyze the influence that the incorporation of plastic waste has on mitigating environmental impacts, as well as the durability properties.