A left-handed metamaterial based on a bianisotropic S-ring resonator is fabricated. By shorting some of the horizontal arms of the paired S-rings, net electric (magnetic) dipoles accumulate under certain magnetic (electric) field induction, which results in a magnetoelectric coupling effect. Free space experimental measurements are carried out and the experimental results demonstrate the cross polarization effect around the left-handed pass band of the metamaterial. The simple planar configuration of the structure also indicates the superiority of this inclusion in the realization of bianisotropic left-handed metamaterials.