Probably have to wait for Draftsight to release an update for AutoCAD 2013. I have no idea how long that will be. It usually takes a few months for the various AutoCAD clones to catch up with a new file version of AutoCAD when released. AutoCAD 2013 is a new DWG file architecture (the last change was in 2010).
If you just need to view the file you can use Autodesk DWG TrueView.
If you need a conversion done there may be some folks on the forums who have installed AutoCAD 2013 and can do a file conversion for you. I haven't downloaded AutoCAD 2013 yet to install where I work, otherwise I would offer help with a file conversion.
We found that ACAD can SAVE AS previous vesions of DXF and this works for us.