No, there is no Jewish priesthood today. According to the Old Testament, the only place from which it was appropriate to offer animal sacrifices to God was the Temple in Jerusalem. In A.D. 70 the Temple was destroyed, meaning Jewish priests no longer had a place to sacrifice. Since the Temple is still in ruins today, there is currently no place for sacrifice. Therefore, there is no active priesthood in Judaism.
This does not mean that there are not people who could be called upon to be priests were the Temple rebuilt. Unlike the other tribes of Israel, the tribe of Levi is not thought to have completely lost its identity. Many Jewish people, with names such as Levit, Levin, and Levine, are thought to be of the tribe of Levi. They are given special roles to fill in Jewish synagogue worship because of their priestly heritage. Those with names such as Cohen, Kahan, and sometimes Katz are thought to come from the priestly family within the tribe of Levi.
In recent years there has been discussion of rebuilding the Temple, and much of the discussion has centered around whether it would be possible to rebuild the Temple without destroying the Dome of the Rock, a Muslim shrine built on the Temple Mount in Jerusalem.
Recent archaeological evidence has suggested that the Holy of Holies--the most important chamber of the Temple and the place where the Ark of the Covenant was kept--lay outside the Dome of the Rock, meaning it would be possible to rebuild the Temple, including the site of the Holy of Holies, without disturbing the Dome of the Rock.
Stories have circulated about Jewish men of Levitical descent training in Israel for active service in a restored priesthood. Last year one group of ultra-orthodox Jews even tried to lay a foundation stone for a new Temple.
Not all Jews support the movement to rebuild the Temple. Some have aired concern that if it were rebuilt, they would have to face the problem whether or not to bring back animal sacrifices--an issue many Jews don't want to wrestle with.