"aren't you" is correct and it can be used in written English.
It is used as an interrogative question or as a statement with a rising inflection, implying doubt or disbelief. For example: "You don't remember me, aren't you?".
Exact(59)
"Aren't you ashamed, aren't you embarrassed?
"You're shocked, aren't you?
You're dyslexic aren't you?
"You're kidding, aren't you?
You're single, aren't you?
Why aren't you seething?
"Well, aren't you special!
You're here, aren't you?
You're me, aren't you?
Why aren't you dancing?
Why aren't you married?
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com