The interplay of population dynamics and evolution within ecological communities has been of long-standing interest for ecologists and can give rise to evolutionary cycles, e.g. taxon cycles. Evolutionary cycling was intensely studied in small communities with asymmetric competition; the latter drives the evolutionary processes. Here we demonstrate that evolutionary cycling arises naturally in larger communities if trophic interactions are present, since these are intrinsically asymmetric. To investigate the evolutionary dynamics of a trophic community, we use an allometric food web model. We find that evolutionary cycles emerge naturally for a large parameter ranges. The origin of the evolutionary dynamics is an intrinsic asymmetry in the feeding kernel which creates an evolutionary ratchet, driving species towards larger bodysize. We reveal different kinds of cycles: single morph cycles, and coevolutionary and mixed cycling of complete food webs. The latter refers to the case where each trophic level can have different evolutionary dynamics. We discuss the generality of our findings and conclude that ongoing evolution in food webs may be more frequent than commonly believed.