AWS S3 Static website API proxying

I'm hosting a static site on some VPS and would like to move everything over to S3 and use static website hosting. Currently I'm proxying /api requests using nginx to my API server like so:

http://ift.tt/1NUUcBa -> http://ift.tt/1iCYCAN

I'm doing this because I have Facebook login on the client and need the same domain to have the cookie transfer to my API for login etc.

I can see that it's possible to create a Route which changes /api to api.website.com/api but it needs to be proxied to maintain the same URL (browser will see a request to www.website.com/api being made)