Virginia is a right to work state. Companies can reject you for whatever reason they deem appropriate. Some companies do not hire if an individual has been charged with a crime. The charge will still show up, but you have not been convicted. It is up to the company to determine whether a charge makes a difference. Typically it doesn't and the company gives you a chance to explain.
Please note that this response is based upon the limited information available in the question. In addition, it is not intended to create an attorney/client relationship and is offered only as general information and not as legal advice.
Yes, companies can reject you for any reason. You should petition to have your charge expunged from your record. Once the expungement is complete, you can legally answer "no" to the question of "Have you ever been arrested."