All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
What is reported from the righteous predecessors in terms of making Ruqyah with the Quran is that they used to recite the Quran before the sick person as Abu Sa‘eed Al-Khudri did with the person who was stung. Ibn Al-Qayyim mentioned that scholars also stated that it is permissible to recite Quranic verses over water, then, the ill person drinks that water. They also stated that it is permissible to write down Quranic verses on a board or a piece of paper then one washes it and drinks that water.
Burning Quranic verses has not been reported to be a practice of the righteous predecessors but they used to burn it or any paper containing the Mention of Allaah out of protecting it from misuse.
As for burning it in order to make Ruqyah for a sick person, we advise you to avoid this act because there is no evidence transmitted from the righteous predecessors – according to my knowledge – supporting this act. Ruqyah with the Quran is an act of worship; so, we cannot add anything to that which was not done by the righteous predecessors. Furthermore, burning papers to make Ruqyah is one of the customs of the jugglers, sorcerers and Christians.
Allaah Knows best.