اللَّهُمَّ ارْحَمْنِي بِالْقُرْآنِ وَاجْعَلْهُ لِي إِمَامًا وَنُورًا وَهُدًى وَرَحْمَةً
Allahummar-hamni bil-Quran waj'alhu li imaman wa nuran wa hudan wa rahmah
O Allah, have mercy on me through the Quran, and make it for me a guide, a light, a source of guidance, and a mercy.
It is Sunnah to make du'a after completing a reading of the entire Quran (khatm). Ramadan is when many Muslims complete one or more readings. This is one of the recommended du'as — asking Allah to make the Quran transform your life, not just words you recited.
Related Du'as
ذَهَبَ الظَّمَأُ وَابْتَلَّتِ الْعُرُوقُ وَثَبَتَ الْأَجْرُ إِنْ شَاءَ اللَّهُ
The thirst is gone, the veins are moistened, and the reward is confirmed, if Allah wills.
Hasanاللَّهُمَّ سَلِّمْنِي لِرَمَضَانَ وَسَلِّمْ رَمَضَانَ لِي وَتَسَلَّمْهُ مِنِّي مُتَقَبَّلًا
O Allah, keep me safe for Ramadan, keep Ramadan safe for me, and accept it from me.
Hasanإِنِّي صَائِمٌ إِنِّي صَائِمٌ
I am fasting, I am fasting. (Say this when provoked while fasting.)
Sahihتَقَبَّلَ اللَّهُ مِنَّا وَمِنْكُمْ
May Allah accept from us and from you.
Hasan