Extension:InviteSignup

The InviteSignup extensions allows account creation to be offered to a user on a closed wiki where it's restricted.

The extension adds a Special:InviteSignup special page, available to users with  permission.
 * The inviter, from this page, by entering just an e-mail address, can quickly invite a single person to create an account on the wiki.
 * The person can then set a username and password, confirming the creation of the account, which is logged; until then, no account is created.
 * The inviter can optionally set additional user groups to which the account will be added automatically after creation.

Installation
You will also have to create a new variable $wgISGroups containing an arry of group where the user can be setup : $wgISGroups = array('user');