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 what you meant is clear evidence from the Quran that touching a marriageable woman is forbidden then there is no text in this regard, however, there is evidence in the Quran about things that are less serious than touching a woman, so it can be understood that touching a woman is more prohibited. Allaah Says (which means): {Tell the believing men to lower their gaze (from looking at forbidden things and guard their private parts (from illegal sexual acts). That is purer for them. …}[Quran 24:30-31]. Allaah further Says (which means): {…do not be soft in speech [to men], lest he in whose heart is disease should covet, but speak with appropriate speech.}[Quran 33:32]. Thus if a man is prohibited from looking and the woman is prohibited from speaking in a soft voice with a marriageable man because that leads to tempting him, then the prohibition of touching is more confirmed as it causes even a greater temptation. There are other examples in this regard.
It should also be noted that the confirmed narrations of the Prophet are evidence as the Quran is evidence. Allaah Says (which means): {And whatever the Messenger has given you—take; and what he has forbidden you—refrain from.}[Quran 59:7]. Furthermore, it is confirmed that the Prophet said: "Beware! I have been given the Quran and something like it. (i.e. the Sunnah)." [Ahmad] So it is not permissible for a Muslim to just refer to the Quran and not refer to the Prophetic narrations. Besides, the Prophet said: "If one of you were to be stabbed in the head with an iron needle, it would be better for him than touching a woman whom he is not permitted to touch."
Allaah Knows best.