I can't find anything in documentation either. However, there are other options other than REST API to get media files in.
1: Since you can send Attachment Files VIA rest, you could send files via an attachment REST create then use either a custom hook to translate those attachments to the media library
2: Since the Media library is files (with a database tag), you could setup an FTP to the existing site and pull the files down, then via API go through the files and if it hasn't been imported into the database, import it.
3: Create a task that takes either a single URL or a list of URLs for the file and both grabs the file and enters it into the database.
the code to import is something like this (may need to modify). It should be noted that at least for 8, when you download a file, then import it into the database, it tends to re-create the file, so i would download the physical file to a temp drive, then import it into the right spot.
CMS.IO.DirectoryHelper.EnsureDiskPath(fullPath, rootDocPath);
int assetLibraryID = CMS.MediaLibrary.MediaLibraryInfoProvider.GetMediaLibraryInfo("Assets", "GlobalContent").LibraryID;
// Download to a temporary path, when we insert into database it re-creates the doc.
System.Net.WebClient webClient = new System.Net.WebClient();
if (System.IO.File.Exists(fullPath))
{
// Replace file and update the Media Library Info
System.IO.File.Delete(fullPath);
webClient.DownloadFile(fileUrl, fullPath);
var UpdatedFileInfo = CMS.MediaLibrary.MediaFileInfoProvider.GetMediaFileInfo(assetLibraryID, combinedPath.Replace("\\", "/") + "/" + FileName);
var newFile = new System.IO.FileInfo(fullPath);
UpdatedFileInfo.FileSize = newFile.Length;
UpdatedFileInfo.Update();
}
else
{
// Upload to temporary folder, then create database Media File and set proper path.
webClient.DownloadFile(fileUrl, uploadPath);
var newFileInfo = new CMS.MediaLibrary.MediaFileInfo(uploadPath, assetLibraryID);
newFileInfo.FilePath = combinedPath.Replace("\\", "/") + "/" + FileName;
newFileInfo.Insert();
// Delete temporary file
System.IO.File.Delete(uploadPath);
}