Phages express anti-CRISPR (Acr) proteins to inhibit CRISPR-Cas systems that would otherwise destroy their genomes. Most acr genes are located adjacent to anti-CRISPR-associated (aca) genes, which encode proteins with a helix-turn-helix DNA-binding motif. The conservation of aca genes has served as a signpost for the identification of acr genes, but the function of the proteins encoded by these genes has not been investigated. Here we reveal that an acr-associated promoter drives high levels of acr transcription immediately after phage DNA injection and that Aca proteins subsequently repress this transcription. Without Aca activity, this strong transcription is lethal to a phage. Our results demonstrate how sufficient levels of Acr proteins accumulate early in the infection process to inhibit existing CRISPR-Cas complexes in the host cell. They also imply that the conserved role of Aca proteins is to mitigate the deleterious effects of strong constitutive transcription from acr promoters.