Copper is an inexpensive material that has found wide application in electronics due to its remarkable electric properties. However, the high toxicity of both copper and copper oxide imposes restrictions on the application of this metal as a material for bioelectronics. One way to increase the biocompatibility of pure copper while keeping its remarkable properties is to use copper-based composites. In the present study, we explored a new copper–ruthenium composite as a potential biocompatible material for bioelectrodes. Sample electrodes were obtained by subsequent laser deposition of copper and ruthenium on glass plates from a solution containing salts of these metals. The fabricated Cu–Ru electrodes exhibit high effective area and their impedance properties can be described by simple R-CPE equivalent circuits that make them perspective for sensing applications. Finally, we designed a simple impedance cell-based biosensor using this material that allows us to distinguish between dead and alive HeLa cells.