My school tuition was due in 2021. However, I paid it in 2022. Can I still claim it on my taxes for this year? Or do I have to wait for next year?

You have to wait until next year.

You can only claim education expenses actually paid during the tax year.

Q. My school tuition was due in 2021. However, I paid it in 2022. Can I still claim it on my taxes for this year? Or do I have to wait for next year?

A. No. As others said, You can only claim education expenses actually paid during the tax year.

Whether you can claim it in 2022 depends on whether the payment was for 2021 classes or the 2022 term.  Usually the payment must match the year of the classes*.  So, if you were late paying for 2021, you cannot count it in either year. 

*There's one exception: you may count money paid, the year before, for classes starting in the first quarter of the following year.