We experimentally investigate the effects of phase noise on the resonant and non-resonant dynamics of the atom-optics kicked rotor. Employing sinusoidal phase modulation at various frequencies, resonances are found corresponding to periodic phase shifts, resulting in the effective transformation of quantum anti-resonances into resonances and vice-versa. The stability of the resonance is analysed, with the aid of experiments, -classical theory and numerical simulations, and is found to be surprisingly robust against phase noise. Finally we look into the effects of phase noise on dynamical localization and discuss the destruction of the localization in terms of decoherence.