There is this girl I like, we have been talking for a little while and I heard a rumor about her and wanted to make sure it wasn't true.
So I asked a friend to find out so she calls her and said that I said it. So the girl I like gets mad at me and says to stop spreading rumors about her and that she doesn't even want a boyfriend. (this was what the rumor was basically about) So what can I do to make right with this girl again?

Well, in case you hadn't figured it out, it is best to not tell a third party about things that you hear. Because whether you realize it or not, you were in fact spreading the rumour.

The best thing you can do is admit that you were wrong. Tell her this directly. And just let her know that you still want to be friends if she would allow you to earn her trust back. But give her the space she desires and do not bug her. If you two were close and good friends she may eventually forgive you.

However, if you pester her you'll decrease the likelihood that she will forgive you. Simply let her know you realize you were wrong and that you're sorry.

So I will assume this is JR high ( I hope) and you are learning a few lessons.

1. don't listen to rumors
2. don't ask someone friend to talk to them about anything
3. if you want to know something and you can't talk to them direct, then don't talk about it at all.