With employment-at-will, an employee does not guarantee that he will stay on the job for any amount of time. Three days later, I was offered the position.I accepted and gave notice to the company I worked for. Rescinding the offer will be a risk. You can rescind and offer for a positive drug screen or before acceptance. Arizona is an at-will employment state. That means that employment can be terminated at any time with or without cause or notice. Spell out those contingencies in your employment application and offer letter. Can an employer legally withdraw a prospective employee's job offer? In short, the answer is yes.