There are a few free/open source PCB autorouters available however using them has been quite difficult due to a lack of interchange standards. There are at least three available such as MUCS-PCB, gEDA PCB (includes autorouter), and the Topological Autorouter (experimental also part of gEDA PCB).
The QAutorouter provides a solution of building the Specctra DSN import and SES export facilities and a common API for "plug in" autorouter engine modules.
Probably the best PCB autorouter for hobbyists at the moment is FreeRouting.net which supports Specctra DSN import and SES export. It is a very capable and effective PCB autorouter. The KiCAD, gEDA, FreePCB, and Eagle EDA tool sets all support Specctra DSN export and SES import and can use FreeRouting.net. However, while FreeRouting.net is free to use (as in beer) it is still commercial software so hobbyist support is limited in that the source code is not available.
A truly free/open source PCB autorouter has been needed by the hobbyist EDA community for quite some time. If you are skilled software developer and familiar with EDA this would be a great opportunity to help out. Thanks in advance for your time and have a nice day!
PS, please see the original announcement on KiCAD-users mailing list.