Gate-controlled Abaronov-Bohm (AB) experiments are performed with AB-ring samples in the presence of spin-orbit interaction. The magnetoresistance at zero magnetic field shows minima in the whole gate voltage range. The observed minima in magnetoresistance at zero magnetic field can be explained in terms of anti-weak-localization. However, the resistance minima at zero magnetic field exhibits oscillatory behaviors as a function of the gate voltage. The possible reason for this oscillation can be attributed to the phase interference induced by the spin-orbit interaction.