You can call getItem function defined in model of article in below file:
components\com_content\models\article.php
You need to load the model first and call the getItem function by passing article id.
jimport('joomla.application.component.model');
JModelLegacy::addIncludePath(JPATH_SITE.'/components/com_content/models');
$articleModel = JModelLegacy::getInstance( 'Article', 'ContentModel' );
Call the function:
$result = $articleModel->getItem($articleId);
And use the access level:
$result->access;