Increasing circuit complexity within quantum systems based on superconducting qubits necessitates high connectivity while retaining qubit coherence. Classical micro-electronic systemshave addressed interconnect density challenges by using 3D integration with interposers containing through-silicon vias (TSVs), but extending these integration techniques to superconducting quantum systems is challenging. Here, we discuss our approach for realizing high-aspect-ratio superconducting TSVs\textemdash 10 μm wide by 20 μm long by 200 μm deep\textemdash with densities of 100 electrically isolated TSVs per square millimeter. We characterize the DC and microwave performance of superconducting TSVs at cryogenic temperatures and demonstrate superconducting critical currents greater than 20 mA. These high-aspect-ratio, high critical current superconducting TSVs will enable high-density vertical signal routing within superconducting quantum processors.