Tokyo ESP

 Rinka is a financially struggling high school girl living with her single father in Tokyo. One day, while going home from school, she sees a penguin flying in the sky towards the Tokyo Sky Tree. She chases after it only to find fish swimming in the air! One of the fish goes through Rinka and causes her to pass out. She wakes up to find that she has developed the ability to slip through solid objects.

(Source: Crunchyroll)