On-chip capacitors with a variable capacitance, as well as design structures for a radio frequency integrated circuit, and method of fabricating and method of tuning on-chip capacitors. The on-chip capacitor includes first and second ports powered with opposite polarities, first and second electrodes, and first and second voltage-controlled units. Each of the first and second voltage-controlled units is switched between a first state in which the first and second electrodes are electrically isolated from the first and second ports and a second state. When the first voltage-controlled unit is switched to the second state, the first electrode is electrically connected with the first port. When the second voltage-controlled unit is switched to the second state the second electrode is electrically connected with the second port. The on-chip capacitor has a larger capacitance value when the first and second voltage-controlled units are in the second state.