You can find special plugins for AutoCAD that allow users to export their .dwg drawings directly to OBJ format. In case that you do not have access to AutoCAD, you have to use some 3rd party CAD alternatives and might even find dedicated CAD converters that support dwg to obj conversion.
Open DWG file Open OBJ file3D CAD/CAM tool for product development
An online CAD conversion service
A commercial online CAD converter
A 3D CAD translation software