Phosphorylates the deoxyribonucleosides deoxycytidine, deoxyguanosine and deoxyadenosine (PubMed:12808445, PubMed:18377927, PubMed:19159229, PubMed:1996353, PubMed:20614893, PubMed:20637175). Has broad substrate specificity, and does not display selectivity based on the chirality of the substrate. It is also an essential enzyme for the phosphorylation of numerous nucleoside analogs widely employed as antiviral and chemotherapeutic agents (PubMed:12808445). {ECO:0000269|PubMed:12808445, ECO:0000269|PubMed:18377927, ECO:0000269|PubMed:19159229, ECO:0000269|PubMed:1996353, ECO:0000269|PubMed:20614893, ECO:0000269|PubMed:20637175}. This is the function of Ensembl gene identifier ENSG00000156136 (DCK, deoxycytidine kinase).