Allow SVG File Uploads in WordPress Media Library

To allow SVG file uploads through the media library, add the following code to your functions.php file:

function cc_mime_types($mimes) {
  $mimes['svg'] = 'image/svg+xml';
  return $mimes;
}
add_filter('upload_mimes', 'cc_mime_types');

A more detailed explanation can be found in this post.