Yes, there are charter schools that reimburse like the one mom said, and it's a certain amount per year. But they are all different. Some give you nothing but free online curriculum, some let you buy supplies/curriculum. Do some serious research before you jump.
I live in Los Angeles and word is that Sky Mountain gives the most money, with a lot of people going with Golden Valley if the other one is full. Apparently Sky Mountain has a waitlist. The "easy" in is the CAVA K12 program, they give you everything you need and a computer, but I hear its a total headache to deal with, and way too much work. Every single person I know who has done K12 charter has quit homeschooling.
I do homeschool, but I actually belong to what is referred to as a PSP (Private School Satellite Program). It's a fancy term for a private homeschool academy, where I actually pay a modest monthly tuition for them to keep my records and deal with the govt. for me. They also provide curriculum counseling, co-op days, field trips, park days, etc. You can do that on your own, but I like being part of the academy because it's a Christian academy and we meet other families like us. I pay for my own curriculum, but I don't mind, because I buy what I think is best for my kids and don't have to wait for it to be approved. And the activities we do probably wouldn't be paid for by a public charter program anyway (like AYSO, museum visits, private piano lessons, etc.). The public charter programs only pay for activities from a pre-approved vendor most of the time.
So I'm not the best one to give advice about the charter programs, but I would highly encourage homeschooling. It's the best decision I ever made for my kids. They are so much happier and well-rounded, and have so much more time just to be kids and hang out as a family and with other kids and families. I also have noticed something really interesting. All the homeschooled kids I know look adults straight in the eye and aren't afraid to speak on level with adults. I can't say this for most kids, especially teenagers.