The Gemini High-Resolution Optical SpecTrograph (GHOST) is the newest instrument being developed for the Gemini telescopes, in a collaboration between the Australian Astronomical Observatory (AAO), the Herzberg Institute for Astrophysics, National Research Council (HIA-NRC) in Canada, and the Australian National University. This paper describes the design of the fiber optic system, developed by AAO. This system links the GHOST multi-object positioner, mounted on Gemini's Cassegrain focus, with the HIA-NRC developed spectrograph, located in the pier lab, 20 meters below the main observatory floor. The GHOST optical cable consists of 62 fibers, Polymicro FBP53/74/94P (53 μm core, 94 μm polyimide buffer), packed into 8 furcation tubes. The optical fibers are held inside the furcation tubes by friction, with between one and twelve fibers in each of the individual tubes. The furcation tubes are mechanically secured to manifold and anchor assemblies by bonding to integral Kevlar yarn within the tubing. The cable includes an interlock switch, linked to the telescope control system, to halt all telescope motions if the cable becomes overstressed. Fibers are terminated by two integral field units (IFU1 and IFU2), guiding and science slits and a calibration light entry port. Mode scrambling is achieved by mechanical agitation in two orthogonal directions, with adjustable frequency and amplitude of up to 10 Hz and 50 mm, respectively.