I have a two year old daughter & her father is not really active in her life. So one day he asked could he get her,I let him get her. I pick my baby up she is pissy all dirty. Than I get home my daughter had weeps and bruises on her back. I asked her who did it she said he did it. We made a police report but he want show up for court.Question is can I just go to juvenile court and petition for him to sign his rights over?

No, because it is a myth that a parent can sign their rights over. But you can petition that you be granted sole custody and that he gets no visitation.

We made a police report but he want show up for court

What do you mean by that? If he is charged with a crime (or juvenile delinquency, if that's what it is), he doesn't get to choose whether he will show up for court.

Don't let him have her any more. If he files for any type of visitation you have the police report with, I would hope, photos.