We present design, fabrication, and testing of a high-speed all-silicon optical phase modulator in silicon-on-insulator (SOI). The optical modulator is based on a novel silicon waveguide phase shifter containing a metal-oxide-semiconductor (MOS) capacitor. We show that, under the accumulation condition, the drive voltage induced charge density change in the silicon waveguide having a MOS capacitor can be used to modulate the phase of the optical mode due to the free-carrier plasma dispersion effect. We experimentally determined the phase modulation efficiency of the individual phase shifter and compared measurements with simulations. A good agreement between theory and experiment was obtained for various phase shifter lengths. We also characterized both the low- and high-frequency performance of the integrated Mach-Zehnder interferometer (MZI) modulator. For a MZI device containing two identical phase shifters of 10 mm, we obtained a DC extinction ratio above 16 dB. For a MZI modulator containing a single-phase shifter of 2.5 mm in one of the two arms, the frequency dependence of the optical response was obtained by a small signal measurement. A 3-dB bandwidth exceeding 1 GHz was demonstrated. This modulation frequency is two orders of magnitude higher than has been demonstrated in any silicon modulators based on current injection in SOI.