We search for signatures of a distant planet around the two-million-year-old classical T-Tauri star CI Tau hosting a hot Jupiter candidate (M_{p} sin{i} ~ 8.1 M_{Jupiter}) in an eccentric orbit (e ~0.3). To probe the existence of an outer perturber, we reanalyzed 1.3 mm dust continuum observations of the protoplanetary disk around CI Tau obtained by the Atacama Large Millimeter/submillimeter Array. We found a gap structure at ~0.8 in CI Taus disk. Our visibility fitting assuming an axisymmetric surface brightness profile suggested that the gap is located at a deprojected radius of 104.5+/-1.6 au and has a width of 36.9+/-2.9 au. The brightness temperature around the gap was calculated to be ~2.3 K lower than that of the ambient disk. Gap-opening mechanisms such as secular gravitational instability and dust trapping can explain the gap morphology in the CI Tau disk. The scenario that an unseen planet created the observed gap structure cannot be ruled out, although the coexistence of an eccentric hot Jupiter and a distant planet around the young CI Tau would be challenging for gravitational scattering scenarios. The mass of the planet was estimated to be between ~0.25 M_{Jupiter} and ~0.8 M_{Jupiter} from the gap width and depth (0.41 +0.04/-0.06) in the modeled surface brightness image, which is lower than the current detection limits of high-contrast direct imaging. The young classical T-Tauri CI Tau may be a unique system to explore the existence of a potential distant planet as well as the origin of an eccentric hot Jupiter.
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