High-throughput T cell receptor (TCR) sequencing allows the characterization of an individual's TCR repertoire and directly queries their immune state. However, it remains a non-trivial task to couple these sequenced TCRs to their antigenic targets. In this paper, we present a novel strategy to annotate full TCR sequence repertoires with their epitope specificities. The strategy is based on a machine learning algorithm to learn the TCR patterns common to the recognition of a specific epitope. These results are then combined with a statistical analysis to evaluate the occurrence of specific epitope-reactive TCR sequences per epitope in repertoire data. In this manner, we can directly study the capacity of full TCR repertoires to target specific epitopes of the relevant vaccines or pathogens. We demonstrate the usability of this approach on three independent datasets related to vaccine monitoring and infectious disease diagnostics by independently identifying the epitopes that are targeted by the TCR repertoire. The developed method is freely available as a web tool for academic use at tcrex.biodatamining.be.