A plasma circuit was a closed electrical network of a computer system that ran on electro-plasma.
In a hallucination Hoshi Sato experienced in 2152 during her first experience aboard a transporter, Sato attempted to communicate with Jonathan Archer by interrupting a plasma circuit in Archer's ready room to send a SOS in Morse code. T'Pol stated that as the circuit was self-contained, no one outside of the room could have been using it to send a message. (ENT: "Vanishing Point")
In 2372, Kira Nerys informed Gul Dukat that firing a recently installed system-5 disruptor aboard the Groumall had ruptured power relays and plasma circuits all over the ship. (DS9: "Return to Grace")