My construction employer’s policy is to run a background check on all new construction executives. One construction executive job seeker has disclosed that he has a criminal record about 8 or 9 years prior. We made the offer and he has accepted. I am now finding out that he was convicted of assault. What can I ask him about this and can the offer be rescinded based on this information?

You can ask him if the assault conviction had anything to do with his prior employment. Ask questions that will determine if this incident was work related without crossing the line.
Evaluate your construction employer’s policy against such convictions. If you rescind the offer, you may be in for some legal troubles. Consulting an attorney who specializes in employment law is a good idea in this case.
With negligent hire and negligent retention lawsuits resulting in huge settlement amounts, you need to consider this criminal conviction very seriously. On the other hand, you need to ensure that you aren't violating state and federal laws or EEOC regulations.