Not sure about the new version of Blender, but the last version ( I forgot the version number) had a plugin you had to download in order to open and convert DWG. But that might have been taken out because Autodesk is cracking down on software freely offering conversions of DWG, and other CAD formats.
Unfortunately, DWG is Autodesk, and Autodesk is not very friendly about sharing the DWG format with free or opensource software from what I've learned.
EDIT:
I just had a look, and yes, the page where I downloaded the free version of a 3d file converter is gone, now replaced with ones you have to pay for...
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