Is involved in the adaptive response to alkylation damage in DNA caused by alkylating agents. Repairs the methylphosphotriester lesions in DNA by a direct and irreversible transfer of the methyl group to one of its own cysteine residues. The methylation of AdaA by methylphosphotriesters in DNA leads to its activation as a transcriptional regulator that activates the transcription of the ada operon which consists of adaA and adaB, and of the adjacent gene alkA. (2'-deoxyribonucleoside 5'-methylphosphotriester)-DNA + L-cysteinyl-[protein] = 2'-deoxyribonucleotide-DNA + H(+) + S-methyl-L-cysteinyl-[protein] Binds 1 zinc ion per subunit. Up-regulated by methylated AdaA itself in response to the exposure to alkylating agents such as MNNG.