A Jewish boy automatically becomes a bar mitzvah on his 13th birthday, no ceremony is required.
He can have one as an adult.
Jewish boys and men
Yes
First, let's clarify what a bar mitzvah actually is. On a Jewish boy's 13th birthday he becomes a bar mitzvah, there is no ceremony necessary for this to happen, it's automatic. Now, when a boy becomes a bar mitzvah, one of the traditions is for him to publicly read from the Torah as this is a responsibility held by Jewish adults. However, any Jewish male who is not circumcised is not allowed to be the person who reads the Torah portion publicly. Therefore, if a Jewish boy is not circumcised, he cannot participate in the ceremony associated with becoming a bar mitzvah.
There is no ceremony where a Jewish boy must go in order to turn into a man. A Jewish boy is considered an adult for religious purposes, and to be responsible for his own conduct, when he turns 13. Whether he or anybody else does anything about it, or even knows about it. But the event is traditionally an occasion for joy and celebration in Jewish families, and many of them make a big deal of it, to live out their happiness and share it with family and friends. When the boy turns 13, he's called a "Bar Mitzvah". It's incorrect and somewhat gauche to refer to a ceremony or a party as a bar mitzvah, and truly repugnant to say that somebody "got bar-mitzvahed". The boy is the Bar Mitzvah when he turns 13, whether or not anybody even notices, and for a lot of people who care, it's a big event.
A Bar Mitzvah is held at a synagogue. The rabbi talks about the boy and says some prayers. The young boy reads the Haftarah (a portion of the Prophets) and when the service is over, the boy has become a man. After the service, traditionally the bar mitzvahed man has a party at a place where more friends and family show up. It trully is an amazing experience.
Bar Mitzvah.
Those who haven't been Bar or Bat Mitzvahed.
Jewish boys have a Bar Mitzvah at 13 years as a rite of passage.
Girls have Bat Mitzvahs and can technically get a Mitzvah at age of 12. Boy have Bar Mitzvahs and are suppose to get them at 13. In my synagog we all get a Mitzvah at 13 give or take a week or sometimes more depending on the case.
Circumcision and Bar Mitzvah
"Bar Mitzvah" is when a Jewish boy turns 13 and has a celebration to become a full-fledged member of the Jewish Community.