Nucleic acid-based drugs like aptamers have recently demonstrated great therapeutic potential. However, experimental platforms for aptamer screening are costly, and the scarcity of labeled data presents a challenge for supervised methods to learn protein-aptamer binding. To this end, we develop an unsupervised learning approach based on the predicted pairwise contact map between a protein and a nucleic acid and demonstrate its effectiveness in protein-aptamer binding prediction. Our model is based on FAFormer, a novel equivariant transformer architecture that seamlessly integrates frame averaging (FA) within each transformer block. This integration allows our model to infuse geometric information into node features while preserving the spatial semantics of coordinates, leading to greater expressive power than standard FA models. Our results show that FAFormer outperforms existing equivariant models in contact map prediction across three protein complex datasets, with over 10% relative improvement. Moreover, we curate five real-world protein-aptamer interaction datasets and show that the contact map predicted by FAFormer serves as a strong binding indicator for aptamer screening.