Here, we present theory and measurements for a bridge rectifier formed from arrays of graphene self-switching diodes (GSSDs). Despite graphene’s lack of a bandgap and high carrier concentration causing a reduced rectification ratio, the extremely high carrier mobility will allow GSSDs to work at frequencies well into the THz region. Compared with a single SSD array, the bridge rectifier structure allows for full-wave rectification of an AC signal. Here we derive an equation for the voltage output of a bridge rectifier formed from GSSDs, which predicts a quadratic relationship between output voltage and input current. This relationship is confirmed using AC and DC measurements. The fabricated rectifier is found to have a high room temperature intrinsic responsivity of ##IMG## [http://ej.iop.org/images/0957-4484/30/36/364004/nanoab25fdieqn1.gif] {$4395,{rm{V}},{{rm{W}}}^{-{rm{1}}}$} at low frequency and a low noise equivalent power of ##IMG##