We propose a multiplexible kinetic inductance ammeter, which uses a high-quality-factor, superconducting, lumped-element, kinetic inductance resonator as a current sensor, a short, superconducting coplanar waveguide (CPW) for current input, and a CPW transmission line for the sensor readout. The resonator consists of an interdigitated capacitor and a superconducting loop that inductively couples to the input CPW. Current running through the central line of the input CPW generates magnetic fields which are focused into the gaps of the input CPW. These magnetic fields can be measured collectively as the magnetic flux through the superconducting loop. The kinetic inductance of the superconducting loop depends on the screening current for the magnetic flux, so the input current is converted to a change in the frequency of the resonator. We analyze the response and noise of a kinetic inductance ammeter with a high-resistivity NbN loop.