Only under certain very specific circumstances. To begin with, the exam would have to reveal a medical condition that directly affected your ability to do the work- for example, if it is a job requiring you to stay awake at night such as a security guard at a hospital and the exam reveals you have a sleep disorder. Specifically, the exam would have to show that the condition would affect your ability to do the job with or without a reasonable accommodation. If, in the above example, a reasonable accommodation could be made (such as breaks every few hours to get up and take a brief walk) that would enable you to do the job safely, then the exam results are not a legal reason to rescind the offer. The important point is that the potential employer must talk to you about the condition and the work and see whether it will be possible to accommodate the issue.
The Equal Employment Opportunity Commission (EEOC) recently filed suit against a company that rescinded an offer to an employee without determining whether he could do the job. Of the situation, the EEOC stated that “Employers cannot rescind a conditional job offer based on uninformed assumptions regarding an individual’s ability to work…. Once [the employer] learned of the applicant’s medical conditions, it refused to hire him based on preconceived notions. That violates federal anti-discrimination law, and the EEOC will continue to enforce it.”