Recycling of waste polymers for valuable use is important for circular economy and environmental sustainability. This study introduces a novel approach to evaluating the compatibility between waste polymers and asphalt binders using advanced molecular representation models. The solubility parameters of waste polymers were predicted using traditional machine learning (ML) models and geometry-enhanced graph neural network (GeoGNN), respectively. The compatibility index was then calculated based on the absolute difference between the solubility parameters of polymers and asphalt. Results indicate that GeoGNN outperforms traditional ML and other GNN models due to its superior ability to capture complex spatial structures. The study also identifies key molecular descriptors that significantly influence solubility parameters of waste polymers. Given the variability in asphalt binder composition, the most compatible waste polymers differ across binders, making the data-driven approach especially valuable. The GeoGNN model greatly enhances the ability to assess compatibility in the polymer-asphalt system. This complements experimental techniques by integrating geometric information to analyze molecular features uncovering the structure-property relationship of material.