This article describes the development of a Direct-Current (DC) superconducting transformer system for the high current test of superconducting cables. The transformer consists of a core-free 10,464 turn primary solenoid which is enclosed by a 6.5 turn secondary. The transformer is designed to deliver a 50 kA DC secondary current at a DC primary current of about 50 A. The secondary current is measured inductively using two toroidal-wound Rogowski coils. The Rogowski coil signal is digitally integrated, resulting in a voltage signal that is proportional to the secondary current. This voltage signal is used to control the secondary current using a feedback loop which automatically compensates for resistive losses in the splices to the superconducting cable samples that are connected to the secondary. The system has been commissioned up to 28 kA secondary current. The reproducibility in the secondary current measurement is better than 0.05% for the relevant current range up to 25 kA. The drift in the secondary current, which results from drift in the digital integrator, is estimated to be below 0.5 A/min. The system's performance is further demonstrated through a voltage-current measurement on a superconducting cable sample at 11 T background magnetic field. The superconducting transformer system enables fast, high resolution, economic, and safe tests of the critical current of superconducting cable samples.