The crystal and local atomic structure of monoclinic ReO2 (alpha-ReO2) under hydrostatic pressure up to 1.2 GPa was investigated for the first time using both X-ray absorption spectroscopy and high-resolution synchrotron X-ray powder diffraction and a home-built B4C anvil pressure cell developed for this purpose. Extended X-ray absorption fine-structure (EXAFS) data analysis at pressures from ambient up to 1.2 GPa indicates that there are two distinct Re-Re distances and a distorted ReO6 octahedron in the alpha-ReO2 structure. X-ray diffraction analysis at ambient pressure revealed an unambiguous solution for the crystal structure of the alpha-phase, demonstrating a modulation of the Re-Re distances. The relatively small portion of the diffraction pattern accessed in the pressure-dependent measurements does not allow for a detailed study of the crystal structure of alpha-ReO2 under pressure. Nonetheless, a shift and reduction in the (011) Bragg peak intensity between 0.4 and 1.2 GPa is observed, with correlation to a decrease in Re-Re distance modulation, as confirmed by EXAFS analysis in the same pressure range. This behavior reveals that alpha-ReO2 is a possible inner pressure gauge for future experiments up to 1.2 GPa.