A method for asteroid deflection that makes use of a spacecraft moving back and forth on a segment of a Keplerian orbit about the asteroid is described and studied. It is shown that on average the spacecraft can exert a significantly larger force on the asteroid than e.g. a stationary gravity tractor, thereby reducing the time needed to effect the desired deflection of the asteroid. Furthermore, the current method does not require canted thrusters on the spacecraft (unlike a stationary gravity tractor) markedly reducing the amount of fuel needed for a given deflection to be realized. The method also allows for the simultaneous use of several spacecraft, further strengthening the overall tugging effect on the asteroid, and distributing the thrust requirement among the spacecraft.