Transcriptional activator PafBC is the key regulator of the mycobacterial DNA damage response and controls around 150 genes, including genes involved in the canonical SOS response, through an unknown molecular mechanism. Using a combination of biochemistry and cryo–electron microscopy, we demonstrate that PafBC in the presence of single-stranded DNA activates transcription by reprogramming the canonical −10 and −35 promoter specificity of RNA polymerase associated with the housekeeping sigma subunit. We determine the structure of this transcription initiation complex, revealing a unique mode of promoter recognition, which we term “sigma adaptation.” PafBC inserts between DNA and sigma factor to mediate recognition of hybrid promoters lacking the −35 but featuring the canonical −10 and a PafBC-specific −26 element. Sigma adaptation may constitute a more general mechanism of transcriptional control in mycobacteria.