The installation of a Cryogenic Underground Test facility (CUTE) is currently ongoing at SNOLAB. The facility includes a cryogen-free dilution refrigerator which is installed within a drywell at the center of a water tank, and shielded with several layers of low radioactivity lead and ultra-pure copper. CUTE will be used for performance tests, characterization measurements, background tests, and calibrations for the SuperCDMS detector towers within a low background environment. In order to achieve the scientific goals foreseen for the CUTE facility, a dedicated calibration system is required. We are designing a remotely accessible system with a convenient graphical user interface (GUI) for precise and reproducible source positioning. This work describes the design and status of this calibration system for CUTE.