The FASER experiment is a new small and inexpensive experiment that is placed 480 meters downstream of the ATLAS experiment at the CERN LHC. FASER is designed to capture decays of new long-lived particles, produced outside of the ATLAS detector acceptance. These rare particles can decay in the FASER detector together with about 500-1000 Hz of other particles originating from the ATLAS interaction point. A very high efficiency trigger and data acquisition system is required to ensure that the physics events of interest will be recorded. This paper describes the trigger and data acquisition system of the FASER experiment and presents performance results of the system acquired during initial commissioning.