Bridge sensors are widely used in military and civilian fields, and their demand gradually increases each year. Digital sensors are widely used in the military and civilian fields. High-precision and low-power analog-to-digital converters (ADCs) as sensor read-out circuits are a research hotspot. Sigma-delta ADC circuits based on switched-capacitor topology have the advantages of high signal-to-noise ratio (SNR), good linearity, and better compatibility with CMOS processes. In this work, a fourth-order feed-forward sigma-delta modulator and a digital decimation filter are designed and implemented with a correlated double sampling technique (CDS) to suppress pre-integrator low-frequency noise. This work used an active pre-compensator circuit for deep phase compensation to improve the system’s stability in the sigma-delta modulator. The modulator’s local feedback factor is designed to be adjustable off-chip to eliminate the effect of process errors. A three-stage cascade structure was chosen for the post-stage digital filter, significantly reducing the number of operations and the required memory cells in the digital circuit. Finally, the layout design and engineering circuit were fabricated by a standard 0.35 μm CMOS process from Shanghai Hua Hong with a chip area of 9 mm2. At a 5 V voltage supply and sampling frequency of 6.144 MHz, the modulator power consumption is 13 mW, the maximum input signal amplitude is −3 dBFs, the 1 Hz dynamic range is about 118 dB, the modulator signal-to-noise ratio can reach 110.5 dB when the signal bandwidth is 24 kHz, the practical bit is about 18.05 bits, and the harmonic distortion is about −113 dB, which meets the design requirements. The output bit stream is 24 bits.