Can I associate a static IP address with my Amazon CloudFront distribution?
CloudFront doesn't support assigning a static IP address to distributions.
When a user requests content from CloudFront, DNS returns 4 IP addresses of the edge location with the lowest latency. This allows content to be delivered with the best possible performance. Since edge locations are associated with different sets of IP addresses, you don't receive the same static address for your distribution when making a request.