DNA nanotechnology has enabled the creation of supramolecular machines, whose shape and function are inspired from traditional mechanical engineering as well as from biological examples. As DNA inherently is a highly charged biopolymer, the external application of electric fields provides a versatile, computer-programmable way to control the movement of DNA-based machines. However, the details of the electrohydrodynamic interactions underlying the electrical manipulation of these machines are complex, as the influence of their intrinsic charge, the surrounding cloud of counterions, and the effect of electrokinetic fluid flow have to be taken into account. In this work, we identify the relevant effects involved in this actuation mechanism by determining the electric response of an established DNA-based nanorobotic arm to varying design and operation parameters. Borrowing an approach from single-molecule biophysics, we determined the electrical torque exerted on the nanorobotic arms by analyzing their thermal fluctuations when oriented in an electric field. We analyze the influence of various experimental and design parameters on the "actuatability" of the nanostructures and optimize the generated torque according to these parameters. Our findings give insight into the physical processes involved in the actuation mechanism and provide general guidelines that aid in designing and efficiently operating electrically driven nanorobotic devices made from DNA.