Can I map to Body Summary in Feeds Importer?
Couple of ways of doing this using a dummy field. Create a dummy text field on the content type you are importing to. Then you could:

a. Use rules to move the dummy field into the body summary.

or

b. (preferred) Use the feeds presave hook in your own module to set the summary AND set the dummy field blank.

/**
 * Invoked before a feed item is saved.
 *
 * @param $source
 *  FeedsSource object that describes the source that is being imported.
 * @param $entity
 *   The entity object.
 * @param $item
 *   The parser result for this entity.
 */
function [YOUR_MODULE_NAME]_feeds_presave(FeedsSource $source, $entity, $item) {
  if ($entity-&gt;feeds_item-&gt;entity_type == 'node' &amp;&amp; isset($entity-&gt;field_temp_summary['und'][0]['value'])) {
    $entity-&gt;body['und'][0]['summary'] = $entity-&gt;field_temp_summary['und'][0]['value'];
    unset($entity-&gt;field_temp_summary);
  }
}