A new data acquisition (DAQ) system for the 200 MeV proton-carbon polarimeter at the Brookhaven National Laboratory Linac was commissioned during the RHIC polarized proton Run 2024. The polarimeter measures the asymmetry of a vertically polarized 200 MeV proton beam scattering off a thin carbon target at scattering angles of 12$^\circ$ and 16.2$^\circ$. For elastic scattering at 16.2$^\circ$, the analyzing power approaches 100%, enabling precise absolute calibration of the beam polarization. To optimize the isolation of elastic events, a variable-thickness copper absorber is employed. The new DAQ system utilizes 14-bit, 200 MHz waveform digitizers (WFDs) to record full \(\sim\!300\,\mathrm{\mu{s}}\) signal waveforms from scintillator detectors during beam bunches. Comprehensive data analysis is performed between beam bunches, which typically repeat every 4.2 s, with processing completed in less than 50 ms. This dead-time-free operation ensures accurate control of systematic errors (\(\lesssim\!0.1\%\)) in the measured elastic asymmetry for 16.2$^\circ$ scattering, resulting in a determination of the beam polarization with systematic uncertainties below 0.5%. For a combined analysis of elastic and inelastic events at 12$^\circ$ and 16.2$^\circ$, the statistical accuracy of the measured beam polarization is approximately 0.5% for a one-hour measurement.