Shape memory alloys (SMAs) exhibit unique functionalities due to their superelastic and shape memory properties. The ability to program and alter their shapes following a thermomechanical stimulus makes them highly important materials for a vast number of applications in the aerospace, automotive, biomedical, and robotic sectors. Research on SMAs has largely focused on metallurgical, mechanical, structural, or phase transformation properties. Here, we investigate the electrical, magnetic, and thermodynamic properties of the biocompatible SMA, Ti₆₇Zr₁₉Nb_11.5Sn_2.5 (at. %). In particular, we report the discovery of a superconducting phase transition with a critical temperature of 4.65 K with 0 K critical magnetic fields of H_c1=13.7mT and H_c2=9.2T. From the temperature dependence of the specific heat and local magnetic field measurements using transverse field muon spin rotation, we also determine a superconducting coherence of 6 nm and a London penetration depth of 776 nm. The results are key towards the development of cryogenic electrical device applications of SMA materials.