This does not mean that such a situation should be handled unkindly or that the person's dignity should be disrespected. Confidentiality should be maintained and the applicant should be informed in a matter-of-fact and considerate manner.
You could say something like this: "It simply is not possible for us to hire you because we have discovered in conducting our routine background check that you are a registered sex offender. If that information is not correct, please tell us so."
It might be a good idea to pause and give the person a moment to respond, if he wishes to do so. Errors do occur--although very rarely. If the person says that the record you received is in error, you should give him the chance to prove that to be the case giving him a definite deadline to produce documentation that proves his contention.
Otherwise, you could conclude with: "We do not sit in judgment here. But I am sure that you can understand that due to the nature of our business and valued customer relationships we must maintain to remain in business, we cannot have someone on our staff with this kind of a conviction on his record. We are sorry that this did not work out differently. We appreciate your interest in working with us and sincerely wish you the best. We want you to know that confidentiality was maintained on this matter and will continue to be maintained by us."