A scalable time jitter measurement module for SNSPDs was designed to address the diverse application requirements of superconducting nanowire single photon detectors (SNSPDs). Based on the analysis of the time jitter measurement principle of the SNSPD system, a digitization unit, a time-to-digital conversion (TDC) unit and a field-programmable gate array (FPGA) unit were designed to digitize the SNSPD output signal, measure the time information and read out the data. The resolution, linearity and time accuracy of the TDC unit of the module were calibrated. The test results show that the resolution of the TDC unit is better than 55 ps, the measurement data is linear and the time accuracy within 100 ns is less than 36 ps. By combining the practical SNSPD system, a time jitter characterization of about 100 ps is achieved. The feasibility of this module for time jitter measurements in SNSPD systems is verified by comparison with a commercial time-correlated single photon counting (TCSPC) module.