Since 1999 a cable test facility at CERN is operational, and each week several 2.5 m long cable samples are tested at 1.9 and 4.3 K and up to 10 T. The current in the samples is supplied by an external 32 kA power supply through a pair of self-cooled copper current leads. In recent years CERN has developed in parallel a 40 kA superconducting transformer, in order to increase the sample current while at the same time reducing the helium consumption. The primary of the transformer, consisting of a 9000 turns solenoidal coil, is wound from a 0.5 mm superconducting wire carrying up to 50 A. The secondary, consisting of 7 turns of LHC cable, is wound directly on top of the primary in order to have a high coupling. The secondary current is measured by integration of the voltage of two Rogowski coils placed around the secondary. Calibration against the 32 kA external power supply has shown that the current in the secondary is known to within 0.5%. With a dedicated feed-back and regulation circuit, any type of current ramp or cycle can be performed. This paper describes the transformer, the current measuring unit, and the current regulation system. Furthermore, results are presented of the first year of operation in the Cable Test Facility.