Adding Automatically To In WordPress Using Filter Referencing?

You can filter the_content and use preg_replace() to look for instances of <table></table> and then surround them with your <div>.

add_action( 'the_content', 'wpse_260756_the_content', 10, 1 );
function wpse_260756_the_content( $content ) {
  $pattern = "/<table(.*?)>(.*?)<\/table>/i";
  $replacement="<div class="table-responsive"><table$1>$2</table></div>";

  return preg_replace( $pattern, $replacement, $content );
}