Is there a way to email a link inviting people to sign up for an event that will be connect to their contact ID?
The contact checksum works equally well for a CiviEvent registration as it does for updating their contact info via a profile.  The tokens page of the wiki has a section at the bottom that shows how to format the URL based on your CMS:

Checksum for Event Registration Pages: To send people to an event registration page use this path where N is the ID of your event:

Drupal: http://www.myorganization.org/civicrm/event/register?reset=1&amp;id=N&amp;{contact.checksum}&amp;cid={contact.contact_id}
Joomla!: http://www.myorganization.org/index.php?option=com_civicrm&amp;task=civicrm/event/register&amp;reset=1&amp;id=N&amp;{contact.checksum}&amp;cid={contact.contact_id}
WordPress: http://www.myorganization.org/?page=CiviCRM&amp;q=civicrm/event/register&amp;reset=1&amp;id=N&amp;{contact.checksum}&amp;cid={contact.contact_id}


Alternate approach: Using checksums  is a little complicated for some folks, especially end users!  To make your life simpler, consider installing the Fancy Tokens extension.  This gives you drop-in tokens for your next several events that include the checksum automatically.