Circularly polarized photons are widely used for conducting experiments to study the magnetic structures of matter. On the basis of superconducting coils developed at the Budker Institute of nuclear physics for a short-period superconducting planar undulator, a superconducting elliptical undulator with a period of ~2.2 cm and an elliptic coefficient of ~ 0.7 is proposed. The poles of the upper and lower halves of the undulator are located at an angle of 45 degrees to each other in the horizontal plane, which creates a periodic vertical and horizontal elliptical field of up to 1 T vertically and 0.7 T horizontally. There is a possibility to create a fast switching left and right polarizations of radiation at a zero angle from two sequentially installed undulators by quickly switching the electron orbit using correction magnets external to the cryostat (up to hundreds of Hertz). A short prototype of an elliptical superconducting undulator was made and magnetic measurements were made in the bath cryostat. The paper presents numerical calculations of the undulator fields, its spectra, and the experimentally measured field.