No. By the halakhic reasoning of Orthodox Rabbi Hershel Schachter, synagogues are not permitted to hire rabbis.
The idea of hiring a professional Jewish minister was copied from Protestant and Catholic Churches. It is not a Jewish institution known in the bible or in the Talmud.
It may actually be better to suffer martyrdom, than for a synagogue to hire a rabbi (yehareg v’al ya’avor), extending the logic of what Rabbi Schachter, a faculty member at Yeshiva University, said last month, to wit, martyrdom is preferable to ordaining a woman as a rabbi because the Conservative movement ordains them.