We report on the manufacturing and testing of the first nanofocusing refractive lenses made of single-crystal silicon carbide. We introduce the fabrication process based on lithography, followed by deep isotropic etching. The lenses were characterized at the energy of 12 keV at the beamline P06 of the synchrotron radiation source PETRA III. A focal spot of 186 nm×275 nm has been achieved with a lens working distance of 29 mm.