Sunnah.com reference : Book 2, Hadith 444English translation : Book 2, Hadith 512Arabic reference : Book 2, Hadith 514
Narrated 'Aishah (RA):
The people complained to Allah's Messenger (ﷺ) of the lack of rain. So, he gave orders for a minbar, which was put for him at the prayer place. He then fixed a day for the people to come out. And he (ﷺ) came out when the edge of the sun appeared, sat down on the Minbar pronounced the greatness of Allah and expressed His praise. Then, he said, "You have complained of drought in your abodes. Allah has ordered you to supplicate Him, and promised that He would answer (your supplications)." Then he (ﷺ) said: All Praise is due to Allah, the Rabb (Lord) of the universe, the Compassionate, the Merciful, the Master of the Day of Judgement; nothing deserves to be worshipped except Allah, Who does what He wills. O Allah! You are Allah, nothing deserves to be worshipped except You; You are the Rich, and we are the poor; send down rain upon us and make what You send down strength and satisfaction for a time." He (ﷺ) then raised his hands and kept rising them till the whiteness of his armpits was visible. He then turned his back to the people and inverted his cloak while keeping his hands raised. He (ﷺ) then faced the people, descended and prayed two Rak'at. Then, Allah produced a cloud and storms of thunder and lightning came and the rain fell.

[Reported by Abu Dawud who graded it Gharib (transmitted through a single narrator), but its chain is Jayyid (good)].
وَعَنْ عَائِشَةَ رَضِيَ اَللَّهُ عَنْهَا قَالَتْ: { شَكَا اَلنَّاسُ إِلَى رَسُولِ اَللَّهِ ‏- صلى الله عليه وسلم ‏-قُحُوطَ الْمَطَرِ, فَأَمَرَ بِمِنْبَرٍ, فَوُضِعَ لَهُ فِي اَلْمُصَلَّى, وَوَعَدَ اَلنَّاسَ يَوْمًا يَخْرُجُونَ فِيهِ, فَخَرَجَ حِينَ بَدَا حَاجِبُ اَلشَّمْسِ, فَقَعَدَ عَلَى اَلْمِنْبَرِ, فَكَبَّرَ وَحَمِدَ اَللَّهَ, ثُمَّ قَالَ: "إِنَّكُمْ شَكَوْتُمْ جَدَبَ دِيَارِكُمْ, وَقَدْ أَمَرَكُمْ اَللَّهُ أَنْ تَدْعُوَهُ, وَوَعَدَكُمْ أَنْ يَسْتَجِيبَ لَكُمْ, ثُمَّ قَالَ: اَلْحَمْدُ لِلَّهِ رَبِّ اَلْعَالَمِينَ, اَلرَّحْمَنِ اَلرَّحِيمِ, مَالِكِ يَوْمِ اَلدِّينِ, لَا إِلَهَ إِلَّا اَللَّهُ يَفْعَلُ مَا يُرِيدُ, اَللَّهُمَّ أَنْتَ اَللَّهُ, لَا إِلَهَ إِلَّا أَنْتَ, أَنْتَ اَلْغَنِيُّ وَنَحْنُ اَلْفُقَرَاءُ, أَنْزِلْ عَلَيْنَا الْغَيْثَ, وَاجْعَلْ مَا أَنْزَلْتَ قُوَّةً وَبَلَاغًا إِلَى حِينٍ" ثُمَّ رَفَعَ يَدَيْهِ, فَلَمْ يَزَلْ حَتَّى رُئِيَ بَيَاضُ إِبِطَيْهِ, ثُمَّ حَوَّلَ إِلَى اَلنَّاسِ ظَهْرَهُ, وَقَلَبَ رِدَاءَهُ, وَهُوَ رَافِعٌ يَدَيْهِ, ثُمَّ أَقْبِلَ عَلَى اَلنَّاسِ وَنَزَلَ, وَصَلَّى رَكْعَتَيْنِ, فَأَنْشَأَ اَللَّهُ سَحَابَةً, فَرَعَدَتْ, وَبَرَقَتْ, ثُمَّ أَمْطَرَتْ }  رَوَاهُ أَبُو دَاوُدَ وَقَالَ: "غَرِيبٌ, وَإِسْنَادُهُ جَيِّدٌ"  1‏ .‏‏1 ‏- حسن.‏ رواه أبو داود (1173)‏، وصححه ابن حبان (2860)‏.‏