Galaxy clusters have been shown, using Faraday rotation of background radio sources, to possess clusterwide magnetic fields of order 1-10 microGauss. These fields can have a variety of important effects on diffusive transport processes in the intracluster medium, and they help to accelerate nonthermal electrons that produce observable diffuse radio emission. However, while plasma mechanisms operating during structure formation readily produce very weak seed fields, how microGauss fields come to exist throughout cluster-size volumes is not clear. Magnetized feedback by the active galaxies known to exist at the centers of many clusters has been suggested as a possible field amplification and distribution mechanism. I will address this model using magnetohydrodynamic simulations of AGN feedback in clusters.