Adding a new category to Joomla (Tested on 3.2) some of the category parameters are dependent on your situation so edit them according to your case (i.e. tag IDs might be different in your database)

gistfile1.txt

<?php
define( '_JEXEC', 1 );
define('JPATH_BASE', dirname(dirname(__FILE__)));
define( 'DS', DIRECTORY_SEPARATOR );
require_once ( JPATH_BASE .DS.'includes'.DS.'defines.php' );
require_once ( JPATH_BASE .DS.'includes'.DS.'framework.php' );
$mainframe =& JFactory::getApplication('site');
$mainframe->initialise();

jimport('joomla.application.component.model');
jimport('joomla.application.component.table');

JTable::addIncludePath(JPATH_SITE.'/administrator/components/com_categories/tables','CategoriesTable');
JModelLegacy::addIncludePath(JPATH_SITE.'/administrator/components/com_categories/models','CategoriesModel');
$categoriesModel = JModelLegacy::getInstance('Category','CategoriesModel');

$category = array();
$category['id'] = 0;
$category['hits'] = 0;
$category['parent_id'] = 10;
$category['extension'] = 'com_content';
$category['title'] = 'Title';
$category['alias'] = 'title';
$category['version_note'] = '';
$category['note'] = '';
$category['description'] = 'some description comes here';
$category['published'] = 1;
$category['access'] = 1;
$category['metadesc'] = '';
$category['metakey'] = '';
$category['created_user_id'] = 0;
$category['created_time'] = '';
$category['modified_user_id'] = 0;
$category['modified_time'] = '';
$category['language'] = '*';
$category['tags'] = array(2,4);
$category['rules'] = array('core.create'=>array('6'=>1,'3'=>1),
				'core.delete'=>array('6'=>1),
				'core.edit'=>array('6'=>1,'4'=>1),
				'core.edit.state'=>array('6'=>1,'5'=>1),
				'core.edit.own'=>array('6'=>1,'3'=>1));
$category['params'] = array('category_layout'=>'','image'=>'');
$category['metadata'] = array('author'=>'','robots'=>'');

$categoriesModel->save($category);
?>