The Talbot self-imaging phenomenon is a fundamental interference effect that is natural to all waves with a periodic structure. We theoretically and experimentally study the Talbot effect for optical waves in the transverse angular domain using whispering-gallery modes of step-index multimode fibers, which carry a high orbital angular momentum and fulfill the required quadratic dispersion relation. By using the complex interference along the core-cladding interface of these fibers, we experimentally demonstrate that the high-order fractional Talbot effect can be used to implement 9- and 30-port beamsplitters using only off-the-shelf components in a compact arrangement. In addition, we show that the beamsplitters can be efficiently interfaced with single-mode fibers, such that our work not only extends the recent developments on the angular Talbot effect to widely available step-index multimode fibers, but also demonstrates a powerful application as a signal multiplexer, which becomes more compact as the number of channels is increased.