Georeferencing DXF using QGIS?

You georeference rasters and affine vectors :)

QGIS has an affine plug-in (qgsAffine) with which you can scale vector layers. You can also apply x and y offsets to all of the vertices in a vector layer if required. I think you will probably need to convert your DXF to a shapefile to use it though (right-click on the layer in the layers panel and go 'Save as...'). Applying rotation to a vector layer is slightly more difficult.

Another - more interactive - option is the Vector Bender plugin. It

does to vectors what georefencers does to raster. This feature is also known as "rubber sheeting".

There is even a video showcasing how it works: https://vimeo.com/96142479

I believe this can be accomplished in QGIS .
However I use cad software with my gis software and would do the following in it.
Either way you need some basic information about the dxf.
1. You should know the units of the dxf.
2. You should have a set of known points in the dxf. (at the very least 2 points).

1a. If the original coordinate system (or non-system) is identifiable then you should transform it to a similar known system.
(if the drawing was just drawn in no system but a 0,0 base system assume some type of equal area.) either alambert or albers (dependent upon the coverage area [size])
2a. ensure that all items in the drawing are displayed (no layers turned off).
3a. select all the features.
4a. move all the features from a known point to a known point.
5a. after determining the original scale resize all selected objects empirically
6a. rotate all selected objects empirically.
Save and/or export the selected objects with a known CRS.