This paper describes the design and testing of an indexing system for optical-beam steering. The cryogenic beam-steering mechanism is a 360-degree rotation device capable of discrete, high-precision alignment positions. It uses low-precision components for its rough alignment and kinematic design to meet its stringent repeatability and stability requirements (of about 5 arcsec). The principal advantages of this design include a decoupling of the low-precision, large angular motion from the high-precision alignment, and a power-off alignment position that potentially extends the life or hold time of cryogenic systems. An alternate design, which takes advantage of these attributes while reducing overall motion, is also presented. Preliminary test results show the kinematic mount capable of sub-arc second repeatability.