Hanks was cited with allegedly making contact with Borthwick's eye or eye area during Exeter's 14-12 Aviva Premiership victory at Sandy Park on Sunday.
The RFU panel, chaired by chief disciplinary officer Judge Jeff Blackett, concluded that the contact had been accidental and the citing was dismissed.
Blackett, who was joined on the panel by Nick Dark and Mike Curling, said in a statement: "The panel concluded that James Hanks' finger did make contact with Steve Borthwick's eye.
"However, the contact occurred in a dynamic situation during a ruck, when James Hanks was driving forward and putting his hand down to prevent him from falling over.
"The contact was entirely accidental."
- Steve Borthwick