The XENON1T liquid xenon time projection chamber is the most sensitive detector built to date for the measurement of direct interactions of weakly interacting massive particles with normal matter. The data acquisition system (DAQ) is constructed from commercial, open source, and custom components to digitize signals from the detector and store them for later analysis. The system achieves an extremely low signal threshold by triggering each channel independently, achieving a single photoelectron acceptance of (93 +/- 3)%, and deferring the global trigger to a later, software stage. The event identification is based on MongoDB database queries and has over 98% efficiency at recognizing interactions at the analysis threshold in the center of the target. A readout bandwidth over 300 MB/s is reached in calibration modes and is further expandable via parallelization. This DAQ system was successfully used during three years of operation of XENON1T.