Yes, it is.
سَالِمًا, يُحَدِّثُ عَنْ أَبِيهِ , قَالَ: قَالَ النَّبِيُّ صَلَّى اللهُ عَلَيْهِ وَسَلَّمَ: «لَا يَمَسَّ الْقُرْآنَ إِلَّا طَاهِرًا»
Salim narrated from his father that the Prophet ﷺ said, ‘None except the pure can touch the Quran.’ (Sunan Daru al-Qutni, 437).
Firstly it is important to clarify that Wudu is not required for reciting Quran, rather it is required for touching the Holy Quran.
In the Hadith above, which is authentic when considering all narrations (see link below), we have clear proof for the Hanafi position that there is a requirement to have Wudu when touching the Holy Quran. However, there is no requirement to have Wudu when a person is indirectly touching the Holy Quran.
وَحَلَّ قَلْبُهُ بِعُودٍ: أَيْ تَقْلِيبُ أَوْرَاقِ الْمُصْحَفِ بِعُودٍ وَنَحْوِهِ لِعَدَمِ صِدْقِ الْمَسِّ عَلَيْهِ. (رد المحتار)
And it is permissible to turn it (a page of the Mushaf) with a stick. Meaning turning the pages of the Mushaf (copy of the Holy Quran) with a stick or something similar, because this cannot be considered touching it (the Mushaf). (Imam Ibn Abideen, Radd al-Muhtaar).
When considering the issue of touching a phone screen many contemporary scholars feel that it is permitted since you are not touching it directly but touching the screen. There may be some difference of opinion regarding this issue, as there often is with contemporary Masail (legal rulings), so a person may choose to take a more cautious approach and insist on Wudu. Regardless of which opinion one follows, it is not acceptable to condemn a Fatwa of credible contemporary scholars unless they clearly contradict that which is mentioned in authoritative books of the Madhab.
It is also important to bear in mind, that the ruling of requiring Wudu is greatly relaxed when we are not dealing with the Mushaf (copy of Quran) itself. In such a case it is permitted to touch the area around the Quranic verse as long as one does not touch the verse directly.
جعلوا المحرم في غير المصحف مس عين القرآن (حاشية على مراقي الفلاح)
They considered the prohibition regarding anything other than the Mushaf (copy of the Quran) to be touching the (verses of) Quran directly. (Imam al-Tahtaawi, Haashiyah ala Maraaqi al-Falah).
لَكِنْ لَا يَحْرُمُ فِي غَيْرِ الْمُصْحَفِ إلَّا بِالْمَكْتُوبِ: أَيْ مَوْضِعُ الْكِتَابَةِ. (رد المحتار)
But with regards to anything other than the Mushaf (copy of the Quran) there is no prohibition on anything except the (place where is Ayah has been) written. Meaning the specific place where the verse is written. (Imam Ibn Abideen, Radd al-Muhtaar).
The entire issue of touching the Mushaf or Quranic verses is relatively detailed, so it is important to study it fully from a reliable book of Fiqh. Unfortunately, many Muslims have turned away from formally studying Islam and rely on Q and A instead, this is not an adequate substitute and thus leads people to misunderstanding aspects of the Deen or a failure in understanding valid and invalid difference of opinion.
And Allah (Most High) Knows Best.
– Answered by Shaykh Noorud-deen (26.05.2021)
Is it sufficient to learn the Deen through questions and answers (Q&A) only?
Is the hadith “seeking knowledge is an obligation upon every Muslim” authentic?
Is it permitted to touch a copy of the Holy Quran without Wudu?
Is it permissible to read Darood from your phone without Wudu?
See also (video):