Recently a incident took place here in India of a rape of young woman.
I saw a status in that it had said that 'O creator if you write the destiny of a girl then please dont write rape in her destiny'
So does Allah(swt) write these kind of incidents in human beings fate or is it Allah(swt) has given the power to do right or wrong and he is going to look on the day of resurrection?

Allah is Just and does not wrong His creatures. Wrongdoing comes from mankind misusing the faculties Allah gave him.