This is long, and based in fact. Also, it's impossible to answer your question without knowing what country/state/province you are working in - as the laws differ depending on location of the work. That said...
If you are in the US, and are in a "work at will" job, then your company is able to change your job and responsibility at will, and you are then in a position to say either, "Yes, I will do this."; or "No, I won't." If you say no, they can fire you, and you can leave for any reason or no reason at all.
However, if you are working under contract or are part of a union your contract or union agreement will dictate what your rights and responsibilities are.
The longer term question I have for your situation is:
Is this company a company that you see yourself working in and eventually doing what you want? If not, then I'd be professional, but very clear that you are interested in the job you were hired for, let them know that you would like to track that career path, and ask if that's a realistic goal. If the answer isn't positive or is a strong "well...maybe", then it could be time to quietly start looking for a company that will support your personal goals.
So to boil it down, your rights are to look for another job and/or do the job for which the company needs. Your options are to continue to work in a job that you don't want - and see if there is a better opportunity to use your training/education, or seek other work.