The Cherenkov radio pulse emitted by hadronic showers of energies in the EeV range in ice is calculated for the first time using full three dimensional simulations of both shower development and the coherent radio pulse emitted as the excess charge develops in the shower. A Monte Carlo, ZHAIRES, has been developed for this purpose combining the high energy hadronic interaction capabilities of AIRES, and the dense media propagation capabilities of TIERRAS, with the precise low energy tracking and specific algorithms developed to calculate the radio emission in ZHS. A thinning technique is implemented to allow the simulation of radio pulses induced by showers up to 10 EeV in ice. The code is validated comparing the results for electromagnetic and hadronic showers to those obtained with GEANT4 and ZHS codes. The contribution to the pulse of other shower particles in addition to electrons and positrons, mainly protons, pions and muons, is found to be below 3% for 10 PeV and above proton induced showers. The characteristics of hadronic showers and the corresponding Cherenkov frequency spectra are compared with those from purely electromagnetic showers. The dependence of the spectra on shower energy and high-energy hadronic model is addressed and parameterizations for the radio emission in hadronic showers in ice are given for practical applications.