Is there any way to add the css class to tinymce inside wysiwyg editor
As you are using wysiwyg module with tinymce library. You should implement the alter function provided by wysiwyg module to add the editor settings.

For tinymce 4.x:

function MYMODULE_wysiwyg_editor_settings_alter(&amp;$settings, $context) {
  if ($context['profile']-&gt;editor == 'tinymce') {
    $settings['link_class_list'] = array(
      "Class Example" =&gt; "class-example",
    );
  }
}


For tinymce 3.x:

function MYMODULE_wysiwyg_editor_settings_alter(&amp;$settings, $context) {
  if ($context['profile']-&gt;editor == 'tinymce') {
    $settings['theme_advanced_styles'] = array(
      "Class Example" =&gt; "class-example",
    );
  }
}


References


documentation of tinymce 4.x
documentation of tinymce 3.x
API of wysiwyg