How to add a permission : reorder Taxonomy terms
You need to implement hook_form_alter  and remove the Sort alphabetically button based on the role.

Edit: Something like this (tested)

function mymod_form_alter(&amp;$form, &amp;$form_state, $form_id) {
  if (in_array('userrole', $user-&gt;roles) &amp;&amp; ($form_id == 'taxonomy_overview_terms') {
    unset($form['actions']['reset_alphabetical']);
    drupal_add_css(drupal_get_path('module','mymod').'/css/mymod.css');
  }
}


and in css/mymod.css, do

.handle,.tabledrag-toggle-weight {display:none;}


This hides the Reset to alphabetical button, drag handles, and Show row weights link.