Phosphorylates the deoxyribonucleosides deoxyadenosine, deoxycytidine and deoxyguanosine with highest activity against deoxycytidine followed by deadenosine and deoxyguanosine (PubMed:27906638). Shows only very minor activity against deoxyuridine and deoxythymidine (PubMed:27906638). 2'-deoxycytidine + a ribonucleoside 5'-triphosphate = a ribonucleoside 5'-diphosphate + dCMP + H(+) 2'-deoxyguanosine + ATP = ADP + dGMP + H(+) 2'-deoxyadenosine + ATP = ADP + dAMP + H(+) kcat is 0.09 sec(-1) with deoxycytodine as substrate. kcat is 3.40 sec(-1) with deoxyguanosine as substrate. kcat is 2.73 sec(-1) with deoxyadenosine as substrate. kcat is 0.29 sec(-1) with deoxythymidine as substrate. kcat is 1.27 sec(-1) with deoxyuridine as substrate. Homodimer. Belongs to the DCK/DGK family.