Yes, but timing matters. According to the Equal Employment Opportunity Commission (EEOC), any personnel or employment records you make or keep (including all application forms, regardless of whether the applicant was hired, and other records related to hiring) must be preserved for one year after the records were made or after a personnel action was taken, whichever comes later. The EEOC extends this requirement to two years for educational institutions and for state and local governments. The Department of Labor also extends this requirement to two years for federal contractors that have at least 150 employees and a government contract of at least $150,000. If the applicant or employee files a charge of discrimination, you must maintain the records until the case is concluded.
The Federal Trade Commission requires that once you've satisfied all applicable recordkeeping requirements, you may dispose of any background reports you received. However, the law requires that you dispose of the reports — and any information gathered from them — securely. This can include burning, pulverizing, or shredding paper documents and disposing of electronic information so that it can't be read or reconstructed.
Source: Background Checks: What Employers Need to Know, http://www.eeoc.gov/eeoc/publications/background_checks_employers.cfm; Disposing of Consumer Report Information? Rule Tells How, http://www.ftc.gov/tips-advice/business-center/disposing-consumer-report-information-rule-tells-how.