POEMMA (Probe of Extreme Multimessenger Astrophysics) Balloon with Radio (PBR) is a balloon-borne experiment being prepared for launch in 2028 from Wanaka, New Zealand, with three key instruments: Fluorescence Camera (FC), Cherenkov Camera (CC), and Radio Instrument (RI). The last detects the signals from atmospheric particle cascades initiated by ultra-high-energy cosmic rays and neutrinos using two dual-polarized sinuous antennas with bandwidth of (60 – 500) MHz accompanied by custom made analog electronics and Data Acquisition System (DAQ) based on a Radio Frequency System-on-Chip (RFSoC) which allows synchronous sampling of all four channels. The radio read-out is triggered externally by the CC with an option for internal triggering currently under development. In addition, two radio transmitting channels (DAC part of the RFSoC) can be used for in situ instrument calibration. The DAQ design and the initial results of its thermal vacuum test are discussed.