We present measurements of the electron ejection direction in the ionization of high (n 90) Rydberg states of rubidium subjected to few-cycle radio-frequency (RF) pulses. For weak pulses we find a strong asymmetry for even (cosine) pulses and no asymmetry for odd (sine) pulses. This asymmetry disappears for pulses longer than four RF cycles. For strong pulses, very large asymmetry is found for both sine and cosine pulses that persists up to eight RF cycles and is attributed to initial state depletion effects within a cycle.