An electrochemically active polymer, polythionine (PTN), was synthesized in natural deep eutectic solvent (NADES) via multiple potential scans and characterized using cyclic voltammetry and electrochemical impedance spectroscopy (EIS). NADES consists of citric acid monohydrate, glucose, and water mixed in the molar ratio of 1:1:6. Electrodeposited PTN film was then applied for the electrostatic accumulation of DNA from salmon sperm and used for the sensitive detection of the anticancer drug epirubicin. Its reaction with DNA resulted in regular changes in the EIS parameters that made it possible to determine 1.0–100 µM of epirubicin with the limit of detection (LOD) of 0.3 µM. The DNA sensor developed was successfully applied for the detection of epirubicin in spiked samples of artificial and natural urine and saliva, with recovery ranging from 90 to 109%. The protocol of the DNA sensor assembling utilized only one drop of reactants and was performed with a minimal number of steps. Together with a simple measurement protocol requiring 100 µL of the sample, this offers good opportunities for the further use of the DNA sensor in monitoring the drug level in biological samples, which is necessary in oncology treatment and for the pharmacokinetics studies of new antitumor drugs.