This is a statue of the Emperor Augustus wearing a toga. Folds of the toga have been raised so it covers his head while he prays or brings sacrifice to one of the gods. For a man to cover his head was to draw attention to his higher social status, as members of the lower classes did not wear togas.
In his letter to the Corinthians, Paul says that any man who prays or prophesies with his head covered dishonours his head (who is Christ) (1 Cor 11:4).