In Naruto series, there are what we called ninja ranks: genin, chuunin, and jounin. To be promoted to a higher ninja rank, you need to passed at least an exam, like in the academy, if you were able to graduate from the academy, you'll be promoted to genin, to be a chuunin ninja, you need to pass the chuunin exam. How about being promoted to Jounin, is there a Jounin exam too? :)
I think this link might help
Here it is said that it is yet unclear if there is an exam.
There is a mention of a Jounin Exam in Kurama Clan Arc (episodes 203 to 207),
and that they are apointed. This info only counts for Naruto anime btw.
It's not clear yet. Maybe there are exams or maybe they are promoted because of their abilities. Sometimes, there are "special-Jounins", which have some special abilities like Anko, Ibiki or Ebisu.