Optical antennas enable the control of light-matter interaction on the nanometer scale. Efficient on-chip electrical switching of plasmonic resonances is a crucial step toward the integration of optical antennas into practical optoelectronic circuits. We propose and numerically investigate the on-chip low-voltage linear electrical tuning of a narrowband optical antenna perfect absorber via a piezoelectric optomechanic cavity. Near unity absorption is realized by an array of gold nanostrip antennas separated from a membrane-based deformable backreflector by a small gap. A narrow linewidth of 33 nm at 2.58 μm is realized through the coupling between the plasmonic mode and photonic mode in the cavity-enhanced antenna structure. An aluminum nitride piezoelectric layer enabled efficient actuation of the backreflector and therefore changed the gap size, allowing for the tuning of the spectral absorption. The peak wavelength can be shifted linearly by 250 nm with 10 V of tuning voltage, and the tuning range is not limited by the pull-in effect. The polarization dependence of the nanostrip antenna coupled with the optomechanic cavity allows the use of our device as a voltage tunable polarization control device.