We describe a dispersive nanoSQUID magnetometer comprised of two variable thickness aluminum weak-link Josephson junctions shunted in parallel with an on-chip capacitor. This arrangement forms a nonlinear oscillator with a tunable 4-8 GHz resonant frequency with a quality factor Q = 30 when coupled directly to a 50 $Omega$ transmission line. In the presence of a near-resonant microwave carrier signal, a low frequency flux input generates sidebands that are readily detected using microwave reflectometry. If the carrier excitation is sufficiently strong then the magnetometer also exhibits parametric gain, resulting in a minimum effective flux noise of 30 n$Phi_0$/Hz$^{1/2}$ with 20 MHz of instantaneous bandwidth. If the magnetometer is followed with a near quantum-noise-limited Josephson parametric amplifier, we can increase the bandwidth to 60 MHz without compromising sensitivity. This combination of high sensitivity and wide bandwidth with no on-chip dissipation makes this device ideal for local sensing of spin dynamics, both classical and quantum.
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