A typical proton CT (pCT) detector comprises a tracking system, used to measure the proton position before and after the imaged object, and an energy/range detector to measure the residual proton range after crossing the object. The Bergen pCT collaboration was established to design and build a prototype pCT scanner with a high granularity digital tracking calorimeter used as both tracking and energy/range detector. In this work the conceptual design and the layout of the mechanical and electronics implementation, along with Monte Carlo simulations of the new pCT system are reported. The digital tracking calorimeter is a multilayer structure with a lateral aperture of 27 cm × 16.6 cm, made of 41 detector/absorber sandwich layers (calorimeter), with aluminum (3.5 mm) used both as absorber and carrier, and two additional layers used as tracking system (rear trackers) positioned downstream of the imaged object; no tracking upstream the object is included. The rear tracker’s structure only differs from the calorimeter layers for the carrier made of ∼200 μm carbon fleece and carbon paper (carbon-epoxy sandwich), to minimize scattering. Each sensitive layer consists of 108 ALICE pixel detector (ALPIDE) chip sensors (developed for ALICE, CERN) bonded on a polyimide flex and subsequently bonded to a larger flexible printed circuit board. Beam tests tailored to the pCT operation have been performed using high-energetic (50–220 MeV/u) proton and ion beams at the Heidelberg Ion-Beam Therapy Center (HIT) in Germany. These tests proved the ALPIDE response independent of occupancy and proportional to the particle energy deposition, making the distinction of different ion tracks possible. The read-out electronics is able to handle enough data to acquire a single 2D image in few seconds making the system fast enough to be used in a clinical environment. For the reconstructed images in the modeled Monte Carlo simulation, the water equivalent path length error is lower than 2 mm, and the relative stopping power accuracy is better than 0.4%. Thanks to its ability to detect different types of radiation and its specific design, the pCT scanner can be employed for additional online applications during the treatment, such as in-situ proton range verification.