When I was 2nd grade my mother lost .5 of the custody of me and I lived with my dad and got to see her on weekends and Thursdays. When I was in 8th grade she convinced me to move in with her so I told my dad I wanted to. She was only trying to get money for her addiction. I didn't realize this at the time. And my father signed his rights away when I moved. I don't like living with my mother anymore she doesn't take care of me. My dad gives me money every week to eat lunch at school she doesn't know that though he pays for my phone and my clothes I would like to live with my father again. My mother is bipolar she always fights me and leaves marks. She calls me names. And runs me off. And I'm 15 now and my dad wants to get his rights back. What do I have to do. Idk what I'll do if I have to stay here longer

... And my father signed his rights away when I moved. ...

Which country are you in?

If it is in the U.S. it would be unlikely that he actually "signed his rights away". But instead signed an agreement that your mother would have primary physical custody. Was there a court order entered, pursuant to that agreement, giving your mother custody? If so, your father should go back to court and ask that the order be modified.

I will agree, he did not most likely 'sign rights away" but merely signed custody over to the mother, (since that is what you wanted) sorry but guess in 8th grade you did not know, and your dad should have refused you.

But you dad hire an attorney and files for custody in court.
The next time she hits you and leaves marks, you call the police and/or report it to your counselor at school.

... and what is her addiction? Has she ever been arrested?

I'm not sure it was a good idea to use your real name, if indeed this is your real name.

At your age you need to be more internet safe.