We demonstrate arbitrary carrier-envelope (CE) phase control of femtosecond laser pulses by an acousto-optic programmable dispersive filter (AOPDF), with an accuracy better than pi/100 at a repetition rate of 1 kHz. We also demonstrate, for the first time to the best of our knowledge, 15 Hz closed-loop CE phase stabilization using an AOPDF inside a 1 kHz chirped pulse amplifier to correct for slow CE phase drifts.