We present the results of the first IceCube search for dark matter annihilation in the center of the Earth. Weakly interacting massive particles (WIMPs), candidates for dark matter, can scatter off nuclei inside the Earth and fall below its escape velocity. Over time the captured WIMPs will be accumulated and may eventually self-annihilate. Among the annihilation products only neutrinos can escape from the center of the Earth. Large-scale neutrino telescopes, such as the cubic kilometer IceCube Neutrino Observatory located at the South Pole, can be used to search for such neutrino fluxes. Data from 327 days of detector livetime during 2011/2012 were analyzed. No excess beyond the expected background from atmospheric neutrinos was detected. The derived upper limits on the annihilation rate of WIMPs in the Earth and the resulting muon flux are an order of magnitude stronger than the limits of the last analysis performed with data from IceCube's predecessor AMANDA. The limits can be translated in terms of a spin-independent WIMP–nucleon cross section. For a WIMP mass of 50 GeV this analysis results in the most restrictive limits achieved with IceCube data.