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, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
The Hadeeth mentioned in the question is invalid and it is inappropriate to attribute this to ‘Aa’ishah, the Mother of the Believers . The following is the origin of this invalid tradition: It was reported that the people of Al-Madeenah complained to ‘Aa’ishah about the drought they were experiencing, therefore, she ordered them to make a hole in the roof of the room above the grave of the Prophet, sallallaahu ‘alayhi wa sallam, in order to remove the barrier between him and heaven. Upon doing this, the rain began to fall until the pasture had grown and their camels had fed.
Commenting on this, Ibn Taymiyyah mentioned that this Hadeeth is Dha‘eef and not adducible. According to the consensus of scholars, the companions used to supplicate Allaah The Exalted for rain either in the mosque or in the desert. This is the lawful way to seek rain by supplicating Allaah The Almighty and asking for His forgiveness. Hence, the tradition in the question is Dha‘eef and invalid.