A DNA sensor has been developed for the determination of doxorubicin by consecutive electropolymerization of an equimolar mixture of Azure B and proflavine and adsorption of native DNA from salmon sperm on a polymer film. Electrochemical investigation showed a difference in the behavior of individual drugs polymerized and their mixture. The use of the copolymer offered some advantages, i.e., a higher roughness of the surface, a wider range of the pH sensitivity of the response, a denser and more robust film, etc. The formation of the polymer film and its redox properties were studied using scanning electron microscopy and electrochemical impedance spectroscopy. For the doxorubicin determination, its solution was mixed with DNA and applied on the polymer surface. After that, charge transfer resistance was assessed in the presence of [Fe(CN)6]3−/4− as the redox probe. Its value regularly grew with the doxorubicin concentration in the range from 0.03 to 10 nM (limit of detection 0.01 nM). The DNA sensor was tested on the doxorubicin preparations and spiked samples mimicking blood serum. The recovery was found to be 98–106%. The DNA sensor developed can find application for the determination of drug residues in blood and for the pharmacokinetics studies.