The movement of magnetic domain walls can be used to build a device known as a shift register, which has applications in memory(1) and logic circuits(2,3). However, the application of magnetic domain wall shift registers has been hindered by geometrical restrictions, by randomness in domain wall displacement and by the need for high current densities or rotating magnetic fields. Here, we propose a new approach in which the energy landscape experienced by the domain walls is engineered to favour a unidirectional ratchet-like propagation. The domain walls are defined between domains with an out-of-plane (perpendicular) magnetization, which allows us to route domain walls along arbitrary in-plane paths using a time-varying applied magnetic field with fixed orientation. In addition, this ratchet-like motion causes the domain walls to lock to discrete positions along these paths, which is useful for digital devices. As a proof-of-principle experiment we demonstrate the continuous propagation of two domain walls along a closed-loop path in a platinum/cobalt/platinum strip.