Booker is a Baptist, but his religious views are broad and pluralistic as described by Dan Gilgoff at US News.
So no, Cory Booker is not a Jew; he is not Jewish. But he is tangled up in Jews, the Bible, and throws around quotations of Hebrew sources, thanks in part to Rabbi Shmuley, according to Shmuley's account of the matter. Here's part of the story from the op-ed.
When he shared with me just a few mornings ago the sad news that his father, Cary, to whom he was particularly devoted, had passed away, Cory expressed his desire to travel together to the grave of the Lubavitcher Rebbe, Rabbi Menachem Schneerson, to pray and light a candle for his father's eternal soul. It was the final days of the campaign and another politician could scarcely have afforded the trip in the middle of the night to the Queens cemetery. But a vigil for his father was the priority and I will never forget watching him recite his father's beloved Psalm 121, slowly and deliberately, enunciating each and every word: "I lift up my eyes to the mountains — whence does my salvation come … from the Lord, Maker of heaven and earth. The Lord watches over you… He will keep you from all harm… He will watch over your coming and going, both now and forevermore."Odd, you say? Hey, it's New Jersey where by state law everybody has to have a shtick.
I asked him if it pained him that his father, a warm and gentle man who took great pride in his son's service, had missed seeing him become a senator by just a few days. "I believe he can see me, Shmuley. He sees me even now."