Fiber-optic interferometric sensors (FOISs) are widely used in seismometers, hydrophones, and gyroscopes. The arctangent approach of phase-generated carrier (PGC-Arctan) demodulation algorithm is one of the key demodulation techniques in FOISs. The conventional PGC-Arctan demodulation algorithm requires the specific value of the phase modulation depth C to work properly. However, C will variate with laser wavelength, temperature, and humidity in the actual working environment, which leads to harmonic distortion and even demodulation failure. In this paper, a novel PGC demodulation algorithm called self-calibration PGC-Arctan (PGC-Arctan-SC) demodulation algorithm is presented. The proposed algorithm can jointly estimate the accurate C value by the elliptical parameters and C-related components while suppressing nonlinear distortion by ellipse fitting algorithm (EFA). Then C can be calibrated to the specific predefined optimal value by the closed-loop proportion integration differentiation (PID) module. The simulation results are consistent with theoretical analysis, and the all-digital PGC-Arctan-SC demodulation system is implemented on the embedded SoC. The experimental results show that C can be estimated and calibrated accurately in real time. The signal-to-noise and distortion ratio (SINAD) of the PGC-Arctan-SC demodulation output achieves 61.57 dB.