A 4×4 Ka-band stacked patch antenna array is designed on a multilayer silicon interposer, operating in 31.7~34.35 GHz, for high-density three-dimensional integration and packaging. A bilayer high-resistivity silicon substrate is employed for prototype fabrication. The measured peak realized gain is 13.98 dBi at 33.1 GHz, with the beamwidths of 20.75° and 27.0° in the E- and H-planes, respectively. The pattern multiplication method is used and validated for calculating the radiation efficiency of the millimeter-wave integrated antenna. The estimated value of radiation efficiency with the measured data is 45.8%.