Activates the transcription of the soxS gene which itself controls the superoxide response regulon. SoxR contains a 2Fe-2S iron-sulfur cluster that may act as a redox sensor system that recognizes superoxide. The variable redox state of the Fe-S cluster is employed in vivo to modulate the transcriptional activity of SoxR in response to specific types of oxidative stress (By similarity). Homodimer.