This article presents a bit-weight calibration technique for successive approximation register (SAR) analog-to-digital converters (ADCs) using a combination of look-up table (LUT) and particle swarm optimization (PSO). The proposed method uses a coordinate rotation digital computer (CORDIC) algorithm to reconstruct LUT and calculate the fitness function (FF). Then, the PSO algorithm is employed to find the global optimum bit weights for SAR ADC to minimize the FF, which increases the convergence speed significantly. In addition, the LUT enables built-in self-test (BIST), allowing measurement cost and time reductions. The effectiveness of the proposed method is validated using 14–20-bit SAR ADC models. Measurement results of a 20-bit SAR ADC demonstrate that after calibration, the signal-to-noise and distortion ratio (SNDR) and spurious free dynamic range (SFDR) are improved by 18.2 and 45.3 dB, respectively. It converges within 15.36 K samples while consuming 36.7 mW.