The space-based gravitational wave detection mission, TianQin, requires high-level synchronization between independent clocks of all spacecrafts to extract the gravitational wave signals. It is necessary to measure the inter-spacecraft relative clock jitter based on laser phase-sideband clock transfer. The main challenge is the tracking and locking of clock sideband beatnote signals with low signal-to-noise ratio and frequency variation. In this paper, a systematic scheme of inter-spacecraft clock jitter readout is reported. The requirement of the clock transfer link for TianQin based on the time-delay interferometry algorithm is derived. A bi-directional laser interferometer system with a transmission optical power below 1 nW and a time delay of ∼50 µs is built up to demonstrate the weak-light clock transfer. In this scheme, frequency modulation is performed on the laser to simulate the inter-spacecraft Doppler frequency shift and its variation. Based on electrical and optical clock transfer comparison experiments, it is demonstrated that the GHz frequency synthesizer is the main noise source below the 50 mHz frequency range. The residual clock jitter noise introduced by the optical transfer link is below 40 fs/Hz1/2 above the 6 mHz frequency range, and the fractional frequency instability is less than 6.7 × 10-17 at 1000 s, which meets the requirement of the TianQin mission. Ultimately, The carrier phase measurement accuracy reaches 1 × 10-4 cycles/Hz1/2 above 6 mHz after differential clock noise correction using measured clock jitter.