Possibly. Again, this will depend on which state you live in. Under federal law, with your permission, the employer can use the credit check as one of the factors in determining the best candidate for the job. It does not matter whether or not the job has anything to do with handling money, juggling budgets, or similar tasks for which credit information might relate more directly to your fitness for the job.
However, if you live in any of the 11 states in which legislation concerning credit checks has been passed (California, Colorado, Connecticut, Delaware, Hawaii, Illinois, Maryland, Nevada, Oregon, Vermont, and Washington), your employer may not use this information to deny you a promotion.