We describe the Short Wavelength Camera (SWCam) for the CCAT observatory including the primary science drivers, the coupling of the science drivers to the instrument requirements, the resulting implementation of the design, and its performance expectations at first light. CCAT is a 25 m submillimeter telescope planned to operate at 5600 meters, near the summit of Cerro Chajnantor in the Atacama Desert in northern Chile. CCAT is designed to give a total wave front error of 12.5 μm rms, so that combined with its high and exceptionally dry site, the facility will provide unsurpassed point source sensitivity deep into the short submillimeter bands to wavelengths as short as the 200 μm telluric window. The SWCam system consists of 7 sub-cameras that address 4 different telluric windows: 4 subcameras at 350 μm, 1 at 450 μm, 1 at 850 μm, and 1 at 2 mm wavelength. Each sub-camera has a 6’ diameter field of view, so that the total instantaneous field of view for SWCam is equivalent to a 16’ diameter circle. Each focal plane is populated with near unit filling factor arrays of Lumped Element Kinetic Inductance Detectors (LEKIDs) with pixels scaled to subtend an solid angle of (λ/D)2 on the sky. The total pixel count is 57,160. We expect background limited performance at each wavelength, and to be able to map < 35(°)2 of sky to 5 σ on the confusion noise at each wavelength per year with this first light instrument. Our primary science goal is to resolve the Cosmic Far-IR Background (CIRB) in our four colors so that we may explore the star and galaxy formation history of the Universe extending to within 500 million years of the Big Bang. CCAT's large and high-accuracy aperture, its fast slewing speed, use of instruments with large format arrays, and being located at a superb site enables mapping speeds of up to three orders of magnitude larger than contemporary or near future facilities and makes it uniquely sensitive, especially in the short submm bands.