One could be simplistic and say that everyone is a negotiator. A more specific response to your question is to say there is not really a profession of negotiator. Lawyers and diplomats are the folks most likely to use negotiation skills as representatives of clients or constituents. Politicians and lobbyists also have to negotiate on behalf of the people or interests they represent. Most reputable business schools require all students to take a course in negotiation.
Some law schools do as well, but mostly the course is an elective rather than a requirement.
That may have to do with the reality that many business school graduates would never have a clue they need to negotiate within the 'narrow confines' they perceive as set out in their job description. One can study negotiation, but, frankly, the best way to learn it is to do it. That's why quality negotiation skills training programs utilize role plays as a teaching tool. Good luck and good negotiating, Steve.