Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
If someone read the verses of sujud at-tilawah while on wudu, let him make sujud at-tilawah. But if he or she are not on wudu, they can still make sujud at-tilawah based on the view of some scholars.
Answering your question about performing wudu for sujud at-tilawah, Sheikh Kifah Mustapha, the Imam and Director of The Prayer Center of Orland Park and representative for Dar El Fatwa of Lebanon in the US, states:
The Quran is the Word of Allah the Almighty revealed on His Prophet Muhammad (peace be upon him).
Reading the Quran is one of the most honorable acts of worship. Allah the Almighty said: {And the Messenger has said, “O my Lord, indeed my people have taken this Qur’an as [a thing] abandoned.} (Al-Furqan 25:30)
In the Quran, there are around 15 verses in which scholars agreed if read, the person should make sujud (prostration). The term is called: Sujud At-Tilawah.
Different Views on wudu for Sujud At-Tilawah
Scholars had different views if such verses were read outside prayer, would a person need to be on wudu to make the Sujud At-Tilawah or not?
The leaders of the four Schools of Fiqh and most scholars required wudu for Sujud At-Tilawah.
But there is another strong view that no wudu is required. This view is attributed to Abdullah Ibn Umar (may Allah be pleased with him) as Imam Al-Bukhari narrates from him. Imam Ibn Taymiyyah supported this view. Contemporary scholars like Ibn Baz and Ibn Uthaymeen also adopted this view.
Wudu for Sujud At-Tilawah
In conclusion, I would say, if someone read such verses while on wudu, let him make Sujud At-Tilawah. But if he or she is not on wudu, they can still make Sujud At-Tilawah based on the view we mentioned.
On another note, some scholars like Imam Al-Qalyubi said, if one was not on wudu or was on wudu but chose not to make Sujud At-Tilawah upon hearing the verse recited, he can say instead: Subhan Allah, Al-Hamdulillah, La Ilaha Illa Allah wa Allah Akbar.
Almighty Allah knows best.