https://aws.amazon.com/api-gateway/faqs/
Q: Can I create HTTPS endpoints?
Yes, all of the APIs created with Amazon API Gateway expose HTTPS endpoints only. Amazon API Gateway does not support unencrypted (HTTP) endpoints. By default, Amazon API Gateway assigns an internal domain to the API that automatically uses the Amazon API Gateway certificate. When configuring your APIs to run under a custom domain name, you can provide your own certificate for the domain.