This comprehensive data set includes the electrical characterization measurements of sputtered Nb/a-Si/Nb Josephson junctions (JJs) for high-speed and high-density superconducting electronics. JJs were studied with critical current densities (Jc) ranging from 0.01 mA/μm^2 to 3 mA/μm^2 and with and without annealing at various temperatures. These properties indicate that Nb/a-Si/Nb Josephson junctions are a potential candidate to extend the speed and circuit density of superconducting electronics to 50 nm diameter (25 mA/μm^2) JJs.