I was angry and texted this girl some pretty mean stuff and she showed her dad. How do I get him to forgive me?

Not enough info. Depends on what you said in the text, why she decided to show it to her father, how well you know her father, whether or not you made threats, etc, etc.
Has she forgiven you?

Sometimes you can't take things back that you do or that you say. That is why thinking before acting is very important. When you have children you are very protective of those children. You showed part of your character and he's probably concerned. I am not sure I would allow you back either depending on what was said.

You man up, apologize for being an immature idiot and HOPE he forgives you. He may NOT. Have you apologized to her? Has she forgiven you? Must have been bad if she told her dad.

Apology may be appropriate, but forgiveness is not guaranteed. They may still want you banned from there life. A life lesson to think before you act or speak.

May I ask how old the daughter and you are? Has she forgiven you? Why do you need the father to forgive you? Are you truly sorry for what you wrote?

You do not mention that you are dating or have any other relationship with the girl. So it is difficult to understand why it is important for you to have the father forgive you. Is the father upset enough about the text(s) that he is talking to other people (such as your parents, school officials or your employer) or are you concerned that he will?

What type of contact do you have with the father? It would determine what form your apology should take. Whether you should call asking to see him in person, send a nice letter, etc. depends on how close you have been.

Frankly, make certain you aren't putting more effort into getting him to forgive than you are his daughter. She is the one you hurt.

You go to him and say you're sorry. Whether he forgives you are not is up to him, but you would have at least made an effort.

I am very worried by someone who asks 'How do I get him to forgive me?'
That is light years away from asking 'How do I ask for forgiveness?'

You don't GET anyone to DO anything in this world, unless you are holding a gun.
Perhaps when you realize that, you won't get into situations like this in the first place.

I thank you all for your answers. We are both 13 and her father demands an apology. I am truly sorry to her and her father and I did say some pretty mean stuff. She is my ex ajd her father has always disliked me though so I am still not sure what to say. I only have an hourand a half before I have to go over to apologize.

She is the one who cheated on me.

Many people try to apologize by saying I am sorry, but...- then go on to justify what they did as being actually out of their control. In other words, they cancel out the apology they just offered.
The saying is something like- "An apology with excuses isn't an apology".

No need to start another thread about the same thing. Do your apology and leave the girl alone. She cheated, you got mad, and now you are being made to apologize. Let this young teen drama end there, and do better by learning from this experience.

'Still not sure what to say.. '

I don't think anyone should coach you. It rarely blurts out right anyway, and if you memorize it, it sounds fake.
An apology should never have excuses in it. That's all. You can even say something to that effect.

You tell him you said some means stuff, you were angry but it does not excuse what you said. Tell him you are truly sorry. Then be done with this and the girl