Can rotten teeth cause acne I have a friend who believes that?

No. There is absolutely no connection between the two.
Not exactly but... Poor dental hygiene can lead to dental abscess and sinus infections which can be serious, and even life threatening. If someone is neglectful of their teeth, they are probably falling short in other hygiene areas as well.
Friend is gullible. The internet and "pop" thinking is full of foolish claims like this. Bad teeth can be fixed, all acne can be managed nowadays, and there is nothing "spiritual" about believing something that somebody imagined or made up.
No. But both can be caused by lifestyles that are not healthy.