Promiscuous editing by CRISPR/Cas systems within the human genome is a major challenge that must be addressed prior to applying these systems therapeutically. In bacteria, CRISPR/Cas systems have evolved in a co-evolutionary arms race with infectious phage viruses that contain inhibitory anti-CRISPR proteins within their genomes. Here, we harness the outcome of this co-evolutionary arms race to engineer an AcrIIA4 anti-CRISPR protein to increase the precision of CRISPR/Cas-based genome targeting. We developed an approach that specifically leveraged (1) protein language models, (2) deep mutational scanning, and (3) highly parallel DNA repair measurements within human cells. In a single experiment, [~]10,000 AcrIIA4 variants were tested to identify lead AcrIIA4 variants that eliminated detectable off-target editing events while retaining on-target activity. The candidates were further tested in a focused round of screening that included a high-fidelity version of Cas9 as a benchmark. Finally, arrayed experiments using Cas9 delivered as ribonucleoprotein were conducted that demonstrated an increase in gene editing precision across two independent genomic loci and a reduction in the frequency of translocation events between an on-target and off-target site. Thus, language-model-guided high-throughput screening is an effective way to efficiently engineer AcrIIA4 to increase gene editing precision, which could be used to improve the fidelity of gene editing-based therapeutics and to reduce genotoxicity.