Catalysis of the reaction: arsenate + reduced glutaredoxin = arsenite + oxidized glutaredoxin. Glutaredoxin functions as the electron donor for arsenate reduction. The electron flow therefore is ( NADPH -> glutathione reductase (EC:1.6.4.2) -> ) glutathione -> glutaredoxin -> arsenate reductase, i.e. glutathione is reduced by glutathione reductase and glutaredoxin is reduced by glutathione.