找到了解决方案。

我找到了一个函数来回答我的问题。

功能如下：

   function get_category_by_letter($letter) {
     $args=array(
       \'orderby\' => \'name\',
       \'order\' => \'ASC\',
       \'hide_empty\' => 0);
       $categories=get_categories($args);

    foreach($categories as $category) {
       $catname = $category->name;
       $first_letter = substr(strip_tags($catname), 0 , 1);

       if(strcasecmp($first_letter,$letter) != 0) continue;
       else {
        $cats[] = $category->term_id;
        $cats[] = $category->name;
     }
    }
    return $cats;

   }