The clockwork mechanism for gravity introduces a tower of massive graviton modes, clockwork gravitons , with a very compressed mass spectrum, whose interaction strengths are much stronger than those of massless gravitons. In this work, we compute the lowest order contributions of the clockwork gravitons to the anomalous magnetic moment, g ? 2 , of muon in the context of an extra dimensional model with a five-dimensional Planck mass, M 5 . We find that the total contributions are rather insensitive to the detailed model parameters and are determined mostly by the value of M 5 . To account for the current muon g ? 2 anomaly, M 5 should be around 0.2?TeV, and the size of the extra dimension has to be quite large, l 5 ? 10 ? 7 ? ? m . For M 5 ? 1 ? ? TeV , the clockwork graviton contributions are too small to explain the current muon g ? 2 anomaly. We also compare the clockwork graviton contributions with other extra dimensional models such as Randall-Sundrum models or large extra dimensional models. We find that the leading contributions in the small curvature limit are universal, but the cutoff-independent subleading contributions vary for different background geometries and the clockwork geometry gives the smallest subleading contributions.
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