The process in which the anatomical structures of a pharyngeal arch artery is generated and organized. The pharyngeal arch arteries are a series of six paired embryological vascular structures, the development of which give rise to several major arteries, such as the stapedial artery, the middle meningeal artery, the internal carotid artery and the pulmonary artery. [ GOC:BHF http://www.ncbi.nlm.nih.gov/pubmed/20122914 GOC:dph ]