Actually she is a Burke-class destroyer which means she does come equipped with the Aegis system for engaging aerial targets. Her main offensive weapon against surface targets would be the Tomahawk cruise missle as indicated by our FRiend, Maquiladora.
Clarification: The Aegis system uses the Standard Missile to engage aircraft. “Aegis” is not the name of a missile though reporting could lead you to believe that it is.