Using WordPress’s add_cap method to Allow Contributors to Upload Media is not Working

I would like to allow contributors to upload media by using the following code added to functions.php. But the Add Media Button still doesn’t show up.

//Allow Contributors to Add Media
if ( current_user_can('contributor') && !current_user_can('upload_files') )
add_action('admin_init', 'allow_contributor_uploads');
function allow_contributor_uploads() {
 $contributor = get_role('contributor');
 $contributor->add_cap('upload_files');
}