Plasmon-resonant nanoparticles with optical scattering in the near-infrared (NIR) are valuable contrast agents for biophotonic imaging and may be detected at the single-particle limit against a dark background, but their contrast is often limited in environments with high noise. Here we consider gyromagnetic imaging as a dynamic mode of optical contrast, using gold nanostars with superparamagnetic cores. The nanostars; exhibit polarization-sensitive NIR scattering and can produce a frequency-modulated signal in response to a rotating magnetic field gradient. This periodic "twinkling" can be converted into Fourier-domain images with a dramatic reduction in background. We demonstrate gyromagnetic imaging of nanostars; inside of tumor cells, using broadband excitation: while their time-domain signals are obscured by incoherent scattering, their Fourier-domain signals can be clearly resolved in less than a second. The gyromagnetically active nanostars do not cause a loss in viability, and can even have a mild stimulatory effect on cell growth.