Legally, job responsibilities could be in a offer letter or (better, from your point of view) an actual employment contract. However, they don't have to be--there is no law requiring it. The company would have to agree to put the responsibilities into some enforceable writte form; if they won't, you can't make them. And if you don't have the resposibilities in an actual written contract, they are not enforceable--the employer may change them at will, since the law of the  land is (in the absence of a contract) "employment at will," which means that the employer controls all aspects of a job. Without a written employment contract, there is no way to protect yourself.