There is no OFCCP rule regarding who can disposition candidates. Anyone on your hiring team could potentially disposition candidates. The most important thing in regard to dispositioning is to do it effectively. That means that someone (recruiter, HR Manager, hiring manager, whoever) should disposition a candidate in a way that gives meaningful information about when and why the candidate dropped out of the selection process.
You can use this OFCCP audit checklist to ensure you're doing what is required to maintain OFCCP's regulations including VEVRAA, Section 503, and EO 11246. Or request a demo to streamline your compliance and recruiting efforts.