A new class of quiescent galaxies harboring possible AGN-driven winds has been discovered using spatially resolved optical spectroscopy from the ongoing SDSS-IV MaNGA survey. These galaxies, termed "red geysers", constitute 5-10% of the local quiescent population and are characterized by narrow bisymmetric patterns in ionized gas emission features. Cheung et al. argued that these galaxies host large-scale AGN-driven winds that may play a role in suppressing star formation at late times. In this work, we test the hypothesis that AGN activity is ultimately responsible for the red geyser phenomenon. We compare the nuclear radio activity of the red geysers to a matched control sample with similar stellar mass, redshift, rest frame NUV - r color, axis ratio and presence of ionized gas. We have used the 1.4 GHz radio continuum data from VLA FIRST survey to stack the radio flux from the red geyser and control samples. In addition to a 3 times higher FIRST detection rate, we find that red geysers have a 5σ higher level of average radio flux than control galaxies. After restricting to rest-frame NUV - r color > 5 and checking mid-IR WISE photometry, we rule out star formation contamination and conclude that red geysers are associated with more active AGN. Red geysers and a possibly-related class with disturbed Hα emission account for 40\% of all radio-detected red galaxies with log (M*MΘ) < 11. Our results support a picture in which episodic AGN activity drives large-scale-relatively weak ionized winds that may provide a feedback mechanism for many early-type galaxies.