In heavy ion radiation therapy, improving the accuracy in range prediction of the ions inside the patient's body has become essential. Accurate localization of the Bragg peak provides greater conformity of the tumor while sparing healthy tissues. We investigated the use of carbon ions directly for computed tomography (carbon CT) to create the relative stopping power map of a patient's body. The Geant4 toolkit was used to perform a Monte Carlo simulation of the carbon ion trajectories, to study their lateral and angular deflections and the most likely paths, using a water phantom. Geant4 was used to create carbonCT projections of a contrast and spatial resolution phantom, with a cone beam of 430 MeV/u carbon ions. The contrast phantom consisted of cranial bone, lung material, and PMMA inserts while the spatial resolution phantom contained bone and lung material inserts with line pair (lp) densities ranging from 1.67 lp cm-1 through 5 lp cm-1. First, the positions of each carbon ion on the rear and front trackers were used for an approximate reconstruction of the phantom. The phantom boundary was extracted from this approximate reconstruction, by using the position as well as angle information from the four tracking detectors, resulting in the entry and exit locations of the individual ions on the phantom surface. Subsequent reconstruction was performed by the iterative algebraic reconstruction technique coupled with total variation minimization (ART-TV) assuming straight line trajectories for the ions inside the phantom. The influence of number of projections was studied with reconstruction from five different sets of projections: 15, 30, 45, 60 and 90. Additionally, the effect of number of ions on the image quality was investigated by reducing the number of ions/projection while keeping the total number of projections at 60. An estimation of carbon ion range using the carbonCT image resulted in improved range prediction compared to the range calculated using a calibration curve.