The SRS is a 2 GeV electron storage ring being built as a dedicated Synchroton Radiation Source at the Daresbury Laboratory. This paper outlines the design of a 3-pole superconducting transverse wiggler magnet for installation in the storage ring. The design field of 5 T will enhance the synchroton radiation spectrum in the region 0.1 to 2 Å. Design constraints imposed by the storage ring geometry and superconductor characteristics are discussed and a specific design based on Nb-Ti superconductor is described.