Advances in adoptive cell immunotherapy have led to several promising options for cancer patients. Single-chain variable fragments (scFvs) were isolated from a human phage display library by panning on recombinant human leukocyte antigen (HLA)-A2-peptide complexes. A scFv (EBNA Clone 315) specific for HLA-A2 carrying a 10 amino acid peptide (LLDFVRFMGV) derived from the Epstein–Barr virus latent protein EBNA3C was fully characterized. EBNA Clone 315 displayed exquisite specificity toward its targeted T-cell epitope (TCE) and did not cross-react with the free peptide, HLA-A2 complexes, which carried irrelevant peptides, or HLA-A2− cells. Furthermore, after engineering into a scFv–Fc fusion protein, we were able to determine its affinity, detection sensitivity, and ability to induce antibody-dependent cellular cytotoxicity (ADCC). As a proof-of-principle, a chimeric antigen receptor (CAR) version of EBNA Clone 315 was used to reprogram NK92MI cells. CAR-expressing NK92MI cells showed highly specific and potent cytotoxicity toward the targeted TCE, with detection sensitivity of approximately 25 molecules and cytolytic capacity threefold greater than scFv-Fc-mediated ADCC. For the first time, we show the successful reprogramming of non-T cells toward a specific TCE using a CAR.