What is the ruling on swearing falsely to avoid falling into the sin of cheating, knowing that the student did not participate in it and erased what he had obtained of the exam questions?

You did well by not cheating and by repenting, but you erred by swearing falsely. You could have denied it without an oath or used dissimulation (tawriya). Your regret over the oath is repentance, so resolve not to return to swearing falsely.