Tracking Call Histories
Yes, this is something CiviCRM can do.

You could create custom fields to track this information and record each (attempted) call as an activity.  Using the activity method, you could even assign a follow up call to a staff member/volunteer if you wanted.  You could use a Profile to simplify the entry of the information.  If you are using Drupal as your CMS, you could create a streamlined webform that integrates with Civi and have a simpler and more specific interface for entry of the call data.