$photo = 'http://zewnetrzny_adres_z_obrazkie.pl/obrazke.jpg';

$wp_filetype = wp_check_filetype(basename($photo), null );
if ( ! function_exists( 'wp_handle_upload' ) ) require_once( ABSPATH . 'wp-admin/includes/file.php' );
$overrides = array( 'test_form' => false);
$file = wp_handle_upload($photo, $overrides);

if ( $file ) {
    echo "File is valid, and was successfully uploaded.\n";
    var_dump( $file);
} else {
    echo "Possible file upload attack!\n";
}

$wp_upload_dir = wp_upload_dir();
$attachment = array(
    'guid' => $wp_upload_dir['path'] . '/' . basename($photo),
        'post_mime_type' => $wp_filetype['type'],
        'post_title' => preg_replace('/\.[^.]+$/', '', $name),
        'post_content' => '',
        'post_status' => 'inherit'
 );

$attach_id = wp_insert_attachment( $attachment, $photo );
require_once(ABSPATH . 'wp-admin/includes/image.php');
$attach_data = wp_generate_attachment_metadata( $attach_id, $photo );
wp_update_attachment_metadata( $attach_id, $attach_data );
add_post_meta($post_id, '_thumbnail_id', $attach_id, true);