T cell receptors (TCRs) are critical components of adaptive immune systems, responsible for responding to threats by recognizing epitope sequences presented on host cell surface. Computational prediction of binding affinity between TCRs and epitope sequences using machine/deep learning has attracted intense attention recently. However, its success is hindered by the lack of large collections of annotated TCR-epitope pairs. Annotating their binding affinity requires expensive and time-consuming wet-lab evaluation. To reduce annotation cost, we present ActiveTCR, a framework that incorporates active learning and TCR-epitope binding affinity prediction models. Starting with a small set of labeled training pairs, ActiveTCR iteratively searches for unlabeled TCR-epitope pairs that are ''worth'' for annotation. It aims to maximize performance gains while minimizing the cost of annotation. We compared four query strategies with a random sampling baseline and demonstrated that ActiveTCR reduces annotation costs by approximately 40%. Furthermore, we showed that providing ground truth labels of TCR-epitope pairs to query strategies can help identify and reduce more than 40% redundancy among already annotated pairs without compromising model performance, enabling users to train equally powerful prediction models with less training data. Our work is the first systematic investigation of data optimization for TCR-epitope binding affinity prediction.