Recently, silicon optical in-phase quadrature (IQ) modulators have played an increasingly important role in coherent optical transmission networks because of their small package size and low cost. To stabilize the modulation performance of the silicon IQ optical modulator (SIQOM), the bias voltages of the SIQOM must be maintained at optimum points. Because of the nonlinear modulation characteristic of the silicon material, it is difficult to achieve high-precision closed-loop control of the bias voltage for the SIQOM. In this paper, a novel automatic bias-control scheme for the SIQOM is proposed and investigated theoretically and experimentally. First, two sinusoidal power dithers with different low frequencies are applied to the channels I and Q biases of the SIQOM. Next, a pair of orthogonal trigonometric functions with the same frequency as the power dither signal is constructed. We find that the optimum point of the bias voltage is the intersection of the orthogonal-integral curves via cross-correlation integral operations between the output signal of the SIQOM and the aforementioned trigonometric functions. The results indicate that the bias errors of the channels I/Q/P relative to the optimum point can be corrected precisely by the proposed scheme, and the jitters of the vector amplitude error caused by this scheme are <1% in 128-Gb/s dual-polarization quadrature phase-shift keying and single-polarization 16-quadrature amplitude modulation formats.