The noncentrosymmetric superconductor, Re₃Ta, has been characterized in detail with a combination of magnetization, heat capacity, and electrical resistivity measurements, as well as a microscopic investigation of the internal magnetic fields using muon spin spectroscopy (μSR). In low applied fields, we observe 100% flux expulsion at a temperature of T_c = 4.68K, which is concomitant with a sudden decrease of the electrical resistivity to zero and a sharp discontinuity in the heat capacity, confirming bulk superconductivity in this material. We find that Re₃Ta is a poor metal, with superconductivity occurring in the dirty limit, and in which the disorder in the structure dominates the physical properties. Zero-field μSR shows that the superconducting state preserves time-reversal symmetry, and transverse-field measurements of the superfluid density are well described by an isotropic s-wave model. A careful analysis of the internal field distribution reveals a high level of disorder in the vortex lattice. Furthermore, we have combined the experimental data and calculated the effective mass, carrier density, and electronic mean-free path in this material, and ultimately show that Re₃Ta lies close to the unconventional region of the Uemura plot.