There are lots and lots of universities that offer programs in Arabic language and culture. Usually the program wouldn’t be in just language, though; you might study language and literature or language and culture (although you could concentrate on Arabic linguistics). Most of the time, these programs are housed within a department of Middle Eastern studies, Near Eastern studies or Islamic studies, so I would search for PhD programs using those terms.
There’s also an old thread on this: http://talk.collegeconfidential.com/college-search-selection/293267-best-islamic-middle-near-eastern-studies-departments.html.