It's not exactly ethical to mull over the sexual orientation of individuals, don't you reckon? Nonetheless, if you must know, Ben Shapiro is a popular political commentator, author, and lawyer. He is often in the public eye due to his views and ideas.
As far as personal life is concerned, he is married to a woman named Mor Toledano and they have three children. So, to answer your query, no, Ben Shapiro is not openly gay.