Is there a way to convert a file to .dwg? I can download a file from Tinkercad as any of these:

.STL
.OBJ
.X3D
.VRML


Is there a way to convert any of those file types to .DWG?
I found this site and tested it a moment ago. I uploaded a simple .STL file (crystal) and had to register as a user (free, unremarkable) in order to perform the conversion.

http://www.cadforum.cz/catalog_en/stl2dwg.asp

The downloaded file was in .DWG format and opened without a problem in AutoCAD 2013 as a 3d object.

Note the placement of the pivot point in Meshmixer (first image) and the corresponding location in AutoCAD.