About this, Wikipedia states:
Excommunication is either a jure (by law) or ab homine (by judicial act of man, i.e. by a judge). The first is provided by the law itself, which declares that whosoever shall have been guilty of a definite crime will incur the penalty of excommunication. The second is inflicted by an ecclesiastical prelate, either when he issues a serious order under pain of excommunication or imposes this penalty by judicial sentence and after a trial.
Excommunication is an act of ecclesiastical jurisdiction, the rules of which it follows. Hence the general principle: whoever has proper jurisdiction can excommunicate, but only his own subjects. Therefore, whether excommunications be a jure (by the law) or ab homine (under form of sentence or precept), they may come from the pope, from the bishop for his diocese; and from regular prelates for religious orders. But a parish priest cannot inflict this penalty. The subjects of these various authorities are those who come under their jurisdiction chiefly on account of domicile or quasi-domicile in their territory; then by reason of the offense committed while on such territory; and finally by reason of personal right, as in the case of regulars. As to excommunications ab homine, absolution from them is reserved by law to the ordinary who has imposed them.
So, yes, an archbishop can excommunicate. Notice however that they do so under the authority given to them by the Pope. The code of Canon Law, number 1442 states:
The Roman Pontiff is the supreme judge for the entire Catholic world; he renders judicial decisions personally, through the ordinary tribunals of the Apostolic See, or through judges he has delegated.