Active control and cancellation of residual amplitude modulation (RAM) in phase modulation of an optical carrier is one of the key technologies for achieving the ultimate stability of a laser locked to an ultrastable optical cavity. Furthermore, such techniques are versatile tools in various frequency modulation-based spectroscopy applications. In this Letter we report a simple and robust approach to actively stabilize RAM in an optical phase modulation process. We employ a waveguide-based electro-optic modulator (EOM) to provide phase modulation and implement an active servo with both DC electric field and temperature feedback onto the EOM to cancel both the in-phase and quadrature components of the RAM. This technique allows RAM control on the parts-per-million level where RAM-induced frequency instability is comparable to or lower than the fundamental thermal noise limit of the best available optical cavities.