I'm sorry , but this sounds like something that Yoda from Star Wars would say. I'm afraid that you can't swap the word order like this. The correct order is: I know that you are a student. And don't forget that you need the article 'a'. Articles are important.

Actually this sentence is perfectly correct. It might not be usual to hear this sentence, but you can put the verb in the beginning and also in the end. It makes sense and everyone would understand it. But I would suggest a comma, and maybe a bit changing the tone of your voice (if you are speaking): "That you are a student, I know." I hope I helped! Ganbatte kudasai! :)