I could not find that anywhere and was curious. I found the relationship between all the other languages and what script, if any, they have. The Aarakocra language seems to have a script because it's listed as you can write in it, but I can not find the script myself, whether it's a separate or a shared script like Dwarvish.
I checked the Elemental Evil where they were introduced, but the script is not mentioned. I've heard that there is something about Aarakocra in Volos Guide to Monsters, but I can not find any mention of them, let alone their language.