We have developed and tested a direct-sampling RF receiver capable of measuring the amplitude of a 1497 MHz sinusoidal beam signal in 0.5 ms integration windows with a relative uncertainty of better than 10 parts per million. The receiver is intended for measuring signals from beam current monitoring cavities on the beamline of the Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab. The beam signal strength, frequency, and integration window fulfill the thus far unmet requirements of the upcoming MOLLER experiment to measure the beam charge for different helicity states.