We show that the evolution of two-component particles under a continuous-time quantum walk can reveal topological phases. A kink in the mean width of the walker distribution signals the closing of the energy gap, a prerequisite for a quantum phase transition between topological phases. For realistic and experimentally motivated Hamiltonians, the distribution in topologically non-trivial phases displays characteristic rings in the vicinity of the origin that are absent in topologically trivial phases. The results are expected to have immediate application to systems of ultracold atoms and photonic lattices, and should aid in the realization of topological states suitable for quantum computation.