I read many times that looking at the Mushaf (text of the Quran) is a required act of worship. Is there any evidence in the Sunnah for this?

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 is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

If looking at the Quran is for the purpose of pondering on it, or revising what one has memorized, or looking for some religious rulings and the like, then this is considered an act of worship and an act by which one gets nearer to Allaah. But if looking at the text of the Quran is not for any of the purposes of worship, then we do not know any evidence which suggests that this is an act of worship.

Allaah Knows best.