if (is_tax() || is_category() || is_tag() ){
    $qobj = get_queried_object();
    // var_dump($qobj); // debugging only

    // concatenate the query
    $args = array(
      'posts_per_page' => 1,
      'orderby' => 'rand',
      'tax_query' => array(
        array(
          'taxonomy' => $qobj->taxonomy,
          'field' => 'id',
          'terms' => $qobj->term_id,
    //    using a slug is also possible
    //    'field' => 'slug', 
    //    'terms' => $qobj->name
        )
      )
    );

    $random_query = new WP_Query( $args );
    // var_dump($random_query); // debugging only

    if ($random_query->have_posts()) {
        while ($random_query->have_posts()) {
          $random_query->the_post();
          // Display
        }
    }
} 

Credit