I'm 13 and I'm in 7th grade now, I am a September baby therefore I could be in 8th grade but I started late. My dad and I have been thinking about moving me up a grade. I'm a straight A student and I'm in advanced classes. Is there any way possible (in Arizona) that I could take online classes during the summer to help me be able to go straight to high school next year?

Have you talked to anyone at your school about making the jump forward? Your principle may be able to recommend how you can achieve that. Congrats on being straight A's. Good Job.

Cutoff dates for entry into school change from time to time and state to state. The chances of skipping a grade now are slim. I too congratulate you on getting straight A's in the 7th grade material. However, the curriculum for 8th grade is different, what makes you believe you would have a sufficient understanding of materials you have never read or been exposed t? In our school 7th graders study Biology while 8th grades study Physics. How would you expect to make up that gap? Do have your dad speak with the principal. I would not bother doing that on your own.

Your dad ( where is your mom?) needs to go to the school and talk to the counselor and then to the Principal. Each school will have its procedure and rules ( even if that rule is no they don't do it) Often you may have to take the national test for your next year, such as take the 8th grade end of the year test and make passing grades in it.
Which gets harder as you get older since it is a lot of info not addressed in earlier years.

You may have to switch to a private school perhaps where they will test you for your proper grade level.

I also go to a Preparatory, which prepares us for college, and us being in middle school; take some high school classes. Which I do for math. And My dad and I were thinking I could do online classes during the summer, if that's possible.

We can't answer your questions. But your school guidance counselor CAN. That is who you should be talking to. The guidance counselor can recommend courses to take or tests to take, that will allow you to move up a grade. This is all specific to your school district's rules. So make an appointment to talk with the counselor today.