How can a cloud-config script copy a file to a server?

You haven't given enough context to know for sure, but for the purposes of this answer I'll assume you're running in Amazon Web Services.

As per the cloud-init documentation here, the only way to create a file directly via cloud-init is to include the file content in the script, either raw, base64-encoded, gzipped or base-64+gzipped.

Apart from doing that, the most straightforward way to do this would be to download the file - either via HTTP or an API call (for example, to S3).

Another way of getting the file onto the server would be to create a custom OS image (AMI) containing the file, by using something like Packer.