  We present a compact current sensor based on a superconducting microwave
lumped-element resonator with a nanowire kinetic inductor, operating at 4.2 K.
The sensor is suitable for multiplexed readout in GHz range of large-format
arrays of cryogenic detectors. The device consists of a lumped-element resonant
circuit, fabricated from a single 4-nm-thick superconducting layer of niobium
nitride. Thus, the fabrication and operation is significantly simplified in
comparison to state-of-the-art approaches. Because the resonant circuit is
inductively coupled to the feed line the current to be measured can directly be
injected without having the need of an impedance matching circuit, reducing the
system complexity. With the proof-of-concept device we measured a current noise
floor {\delta}Imin of 10 pA/Hz1/2 at 10 kHz. Furthermore, we demonstrate the
ability of our sensor to amplify a pulsed response of a superconducting
nanowire single-photon detector using a GHz-range carrier for effective
frequency-division multiplexing.
