How can I add a custom form menu link to the administrative menu programmatically?
Create a new menu using hook_menu. Like this

$items['admin/config/my_form'] = array(
    'title' =&gt; 'My Form',
    'page callback' =&gt; 'drupal_get_form',
    'page arguments' =&gt; array('form_id'),
    'access callback' =&gt; TRUE, // Give access as per your need.
    'type' =&gt; MENU_NORMAL_ITEM,
);


Using this your form will be created with the link / menu item under configuration menu.

Thanks.