In a word, no. I get this question from time to time, and I always feel sad having to give news that often people do not want to hear.
If what you mean by “believe in Jesus” is believe that he is God, or that he rose from the dead, or died for your sins, no. Jews do not believe those things. Jews are strict monotheists – no Trinity – and we do not have any belief in what Christians call “original sin.”
If Jesus is important to you as the Son of God or as your Savior, you aren’t Jewish. That’s OK – we are happy for you to be a good Christian, and we hope you find a branch of Christianity that works for you. Judaism doesn’t have an opinion on a “one true religion,” unlike Christianity and Islam; we believe that there are many different ways to be in relationship with the Holy One. This way is our way, and it does not involve a belief in Jesus as anything but an ordinary guy who died a long time ago. To learn more about what Jews believe about the man from Nazareth, read What Do Jews Believe about Jesus?
If you find that you are attracted to Judaism, but still believe that Jesus is the Christ (the Anointed One) then you are welcome to be a friend to the Jewish community. If you have Jewish ancestors, but Jesus is your Savior, that’s fine – but you aren’t “Jewish,” you are a Christian with a Jewish heritage. That’s wonderful! And we are happy to have that relationship with you.
Someone’s going to jump in here and talk about Messianic Judaism, so I’m going to repeat my policy on that. Messianic Judaism is not Rabbinic Judaism. It’s a form of Christianity in which Jesus is the savior of mankind. What I’m teaching here is Rabbinic Judaism.
For why I dislike terms like “Judeo-Christian:” read The Interfaith Potluck.