Rapid and fine control over the phase of light is demonstrated by transferring digitally generated phase jumps from radio-frequency electrical signals onto light by means of acousto-optic interaction, and the underlying mechanism elucidated. This technique was used to engineer optical phase noise by tailoring the statistics of phase jumps in the electrical signal, which was then quantified using visibility measurements of the interference fringes. Such controlled dephasing finds applications in modern experiments involving the spread or diffusion of light in optical networks. In addition, the zero-delay intensity-intensity correlation [G2(0)] values of light emerging from different ports of a well-stabilized Mach-Zehnder interferometer in the presence of engineered partial phase noise are calculated, and it is shown analytically how the dark port of the interferometer nontrivially becomes a weak source of highly correlated or bunched photons.