Can entries in a category be reordered?
There isn't a builtin way to manually sort the entries as you can in a structure. 

When calling the entries in your templates, you can make use of the 'order' parameter to order the entries returned. From the documentation:


  The order the entries should be returned in. Possible values include
  'title', 'id', 'authorId', 'sectionId', 'slug', 'uri', 'postDate',
  'expiryDate', 'dateCreated', and 'dateUpdated', as well as any textual
  custom field handles. If you want the entries to be sorted in
  descending order, add “desc” after the property name (ex: 'postDate
  desc'). The default value is 'postDate desc'.


For example:

{% entries = craft.entries.section('news').order('postDate').limit(10) %}