Nuclear magnetic resonance (MR) (NMR) is commonly used for the determination of rock porosity, as well as pore size distribution (PSD) and tortuosity, required to handle hydrocarbon exploitation. Emerging technologies for NMR equipment now enable the visualization of porosity using magnetic resonance imaging (MRI). Currently, single‐point imaging is the most common MRI technique employed, but diffusion‐weighted imaging has been attracting the attention of geologists and geophysicists. In this study, a more advanced technique, diffusion tensor imaging (DTI), is proposed for the characterization of rock core samples. The main purpose of this paper is to demonstrate the usefulness of DTI in the petrophysical characterization of rocks and discuss its strengths. As an example, a carbonate core sample was examined using DTI. The diffusion tensor (DT) was obtained and DT parameters (mean diffusivity, MD; fractional anisotropy, FA; three eigenvalues; DT components; and proton density, PD) were visualized in 2D and 3D. Each parameter was described and its utility in terms of pore space characterization was analyzed. In addition, a new parameter, principal diffusion tracts, was introduced based on the DT tractography performed in the study. The analysis is summarized in a set of DT parameters and a resultant ellipsoid that delivers complementary information about the sample's pore network microgeometry, including referential measurements of anisotropic phantoms. The applications of DTI for the determination of pore size distribution, tortuosity and conductivity are also shown. The study ends with a consideration of the potential prospects and challenges for DTI‐based examination of rock core samples.