We studied the flow fields generated inside sessile drops that oscillate periodically between states of high and low contact angle under the influence of alternating electric fields of variable frequency and amplitude. Following the motion of dye patches, we show that the number of oscillation cycles required to achieve mixing scales logarithmically with the Péclet number as expected for chaotic mixing. High speed movies reveal an asymmetry of the drop shape between the spreading and receding phase of the oscillations. This results in net internal flow fields that we characterize by tracing the motion of colloidal seed particles. The strength and frequency dependence of the flow are explained in terms of Stokes drift driven by capillary waves that emanate from the oscillating contact line.