Manual:$wgAllowCopyUploads

Details
Users also need to have the associated user right  before this option is available. By default only administrators (sysops) have this permission.

By default, upload by URL are only possible using the API (or extensions such as UploadWizard). To make the option usable from Special:Upload, you need to set $wgCopyUploadsFromSpecialUpload to true as well.

By default, any source URL location is allowed, but you can whitelist a specific set by using $wgCopyUploadsDomains.

Example usage
This example setup will allow all autoconfirmed users to upload by URL, via Special:Upload or the API. Add to the bottom of your LocalSettings.php: