We describe the motion of an asymmetric dimer across a horizontal surface when exposed to an oscillatory fluid flow. The dimer consists of two spheres of distinct sizes, rigidly attached to each other. The dimer is found to move in a direction perpendicular to the fluid flow, with the smaller sphere foremost. We have determined how the speed depends upon the vibratory conditions, on the fluid viscosity, and on the dimer size and aspect ratio. Computer simulations are used to give an insight into the mechanism responsible for the motion. We use a scaling argument based on the asymmetry of the streaming flow to predict the approximate dependence of the migration speed on the system parameters.