This brief proposes a fully dynamic fourth-order discrete-time delta-sigma ADC using a closed-loop two-stage floating inverter amplifier (FIA) for biosignal acquisition applications. The closed-loop two-stage FIA, using a class-AB FIA as the 1st stage and a self-biased cascoded FIA as the 2nd stage, optimizes the noise performance while achieving more than 65 dB DC gain. A switch-capacitor (SC) integrator with charge sharing module is proposed to reduce the impact of FIA leakage current on the accuracy of the integrator in ADCs for biosignal acquisition applications. Fabricated in a 65 nm deep n-well CMOS process, the prototype, withan active area of $0.35\times 0.34$ mm 2, consumes $3.5~\mu \text{W}$ from a 1.5 V at a 100 kHz sampling frequency. The proposed ADC achieves a signal-to-noise distortion ratio (SNDR) of 102.7 dB and a SNDR-based Schreier figure of merit (FOM) of 183.1 dB.