A high-temperature superconducting cable was successfully tested in a background field of 19.8 T at the National High Magnetic Field Laboratory. The CORC cable was wound from 40 superconducting tapes and had an outer diameter of only 7.5 mm. The cable carried a superconducting current of 4101 A at a temperature of 4.2 K in a background field of 19.81 T, which is the highest superconducting current ever recorded under these conditions. The engineering current density of 93 A/mm2 opens the door for the next generation of superconducting, low-inductance magnets made from CORC cables that operate at magnetic fields exceeding 20 T.