Short answer
Yes. You may read the Quran on a phone or tablet without wudu. Most Hanafi muftis today also allow touching the screen, because the text is light behind glass and is not written on it, though touching only the edges, or having wudu, is better.
Reading the Quran from a screen without wudu is permissible. Holding the device and touching its screen is permissible according to most contemporary Hanafi fatwas, because a screen is not a mushaf and the glass is a barrier; having wudu, or scrolling from the edge, is the more cautious and more respectful way.
The four schools agree on this.
Explanation
The rule of wudu applies to the mushaf, a written copy of the Quran. The Hanafi texts allow touching the mushaf through a separate barrier such as a cloth or a case (see touching the Quran without wudu). On a phone the letters are not written on anything: they appear only while the app is open and vanish when it closes, and the glass sits between your finger and the light. This is why most Hanafi muftis today allow it, and scholars in the other schools take broadly the same view.
Some muftis still advise not touching the part of the screen where the ayat appear when you have no wudu, out of respect. A simple habit covers both views: scroll from the margin, or turn pages with the side buttons.
For a person in janabah the question is not touching but reciting: they may look at the screen and follow with their eyes, but should not recite aloud as Quran until after ghusl. Questions for a woman in her period are in the women section.
Respect still applies to the device while the Quran is open. Close the app before you go into the bathroom (see reciting in the bathroom), do not leave it open on the floor, and think twice about an ayah as your lock screen (Quran wallpapers). AmalKit's Quran reader and recitation tool work on any phone.
The evidence
Quran, Surah Al-Waaqia 56:77-79
إِنَّهُۥ لَقُرْءَانٌۭ كَرِيمٌۭ ﴿٧٧﴾ فِى كِتَٰبٍۢ مَّكْنُونٍۢ ﴿٧٨﴾ لَّا يَمَسُّهُۥٓ إِلَّا ٱلْمُطَهَّرُونَ ﴿٧٩﴾
Indeed, it is a noble Qur'an In a Register well-protected; None touch it except the purified.
The Quran describes itself as a book that only the purified touch, which the four schools take as the basis for needing wudu to touch the mushaf.
Where the ruling is recorded
- al-Hidaya, Kitab al-Taharah, chapter on menstruation and istihadah. The principle that touching through a separate barrier (ghilaf munfasil) is allowed, which contemporary muftis apply to a screen.
- Radd al-Muhtar (Ibn Abidin), Kitab al-Taharah, discussion of what is forbidden to the junub and the one without wudu. Defines what is and is not the mushaf, the basis for treating a screen differently from a printed copy.
This answer is pending review by the scholars on our team. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.