Cleaves single-stranded DNA in a dC-specific manner. The cleavage occurs exclusively at the 5'-proximal position (dC1) within a dCs tract having a minimal size of 6 bases. These specific cleavages may have a detrimental effect on the replication of host dC-containing DNA. Endonucleolytic cleavage of the 5' phosphodiester bond of deoxycytidine in single-stranded DNA.