Hi all, Jerrin from Asana support here.
I do want to state there is a free way to integrate your Google Form with Asana. It works by sending the responses to the Asana project email, which would make a task in the project. You can find instructions on this here: Web Forms & Asana • Asana Product Guide
There is a paid version through tray.io which is mentioned, and the highlight of that is the ability to fill out Custom Fields with your forms.
I hope this helps!