Right to Privacy at Work FAQ
Can my employer require me to take a psychological test before promoting me to management?
3. Can my employer require me to take a psychological test before promoting me to management?
Psychological tests given by employers are often invasive and their purpose questionable. If the employer doesn't seem to have a sound reason for giving the test, and the questions make you uncomfortable, then you might have a legitimate claim that the employer is violating your privacy rights.
For more information on whether employee testing is allowed, see Nolo's article Workplace Testing: What Your Employer May Require.