  We carry out an experimental feasibility study of a magnetic field sensor
based on the kinetic inductance of the high-$T_\mathrm{c}$ superconductor
yttrium barium copper oxide. We pattern thin superconducting films into
radio-frequency resonators that feature a magnetic field pick-up loop. At 77 K
and for film thicknesses down to 75 nm, we observe the persistence of screening
currents that modulate the loop kinetic inductance. According to the
experimental results the device concept appears attractive for sensing
applications in ambient magnetic field environments. We report on a device with
a magnetic field sensitivity of 4 pT/Hz${}^{1/2}$, an instantaneous dynamic
range of 11 $\mu$T, and operability in magnetic fields up to 28 $\mu$T.
