A medium-sized Schwarzchild-Couder Telescope (SCT) is being developed as a possible extension for the Cherenkov Telescope Array (CTA). The Cherenkov camera of the telescope is designed to have 11328 silicon photomultiplier pixels capable of capturing high-resolution images of air showers in the atmosphere. The combination of the large number of pixels and the high trigger rate (> 5 kHz) expected for this telescope results in a multi-Gbps data throughput. This sets challenging requirements on the design and performance of a data acquisition system for processing and storing this data. A prototype SCT (pSCT) with a partial camera containing 1600 pixels, covering a field of view of 2.5 x 2.5 square degrees, is being assembled at the F.L. Whipple Observatory. We present the design and current status of the SCT data acquisition system.