Grab URL as file upload for Drupal 7?
You're looking for the FileField Sources module:


  FileField Sources is an extension to the FileField module. The FileField module lets you upload files from your computer through a CCK field. The FileField Sources module expands on this ability by allowing you to select new or existing files through additional means, including:
  
  
  Re-use files by an auto-complete textfield
  Attach server-side files uploaded via FTP
  Transfer files from a remote server (cURL required)
  Paste a file directly from the clipboard (Drupal 7 only)
  Select existing files through the IMCE file browser
  


Emphasis mine.