© 2017 The MAJORANA Collaboration is searching for the neutrinoless double-beta decay of the nucleus 76Ge. The MAJORANA DEMONSTRATOR is an array of germanium detectors deployed with the aim of implementing background reduction techniques suitable for a 1-ton 76Ge-based search. The ultra low-background conditions require regular calibrations to verify proper function of the detectors. Radioactive line sources can be deployed around the cryostats containing the detectors for regular energy calibrations. When measuring in low-background mode, these line sources have to be stored outside the shielding so they do not contribute to the background. The deployment and the retraction of the source are designed to be controlled by the data acquisition system and do not require any direct human interaction. In this paper, we detail the design requirements and implementation of the calibration apparatus, which provides the event rates needed to define the pulse-shape cuts and energy calibration used in the final analysis as well as data that can be compared to simulations.