<p>Is there any open-source, <code>PHP based</code>, role-based access control system that can be used for <code>CodeIgniter</code>?</p>

phpgacl
http://phpgacl.sourceforge.net/
is a generic acl based access control framework
while I don't know about any CI specific implementation, i know that you only need the main class file to make phpgacl work. So i belive that integration with CI won't be any problem. (I've work passingly with CI)