The space-based gravitational wave detection need to use laser acquisition technique to construct the inter-satellite laser link, and the spot center positioning is the core technique for measurement in the laser acquisition phase. Taking the Taiji program for example, the spot center positioning precision should be less than 0.1 pixel. However, the receiving laser intensity is nearly 100 pW at the detector surface due to the long-distance propagation. The precision of most of the conventional positioning methods is significant degraded under low signal-to-noise ratio conditions, so it is crucial to study how detector noise affects the spot center positioning precision. To address these challenges, we first elucidate the operational principles of laser acquisition and pointing technique, then theoretically analyze the mechanism by which the background noise of CMOS affects the spot center positioning precision and introduce an improved spot center positioning algorithm. Finally, the coupling relationship between different system parameters and the background noise of CMOS is measured through the experiment. The experimental results agree with the theoretical analysis, validating the correctness of the noise model and proving that this algorithm can achieve the measurement precision of 0.018 pixel under weak light conditions.