An enzyme that catalyzes reversibly the phosphorylation of deoxycytidine with the formation of a nucleoside diphosphate and deoxycytidine monophosphate. Cytosine arabinoside can also act as an acceptor. All natural nucleoside triphosphates, except deoxycytidine triphosphate, can act as donors. The enzyme is induced by some viruses, particularly the herpes simplex virus (HERPESVIRUS HOMINIS). EC 2.7.1.74.