Because you're using vanilla ACAD, you don't have access to coordinate reference systems or the ability to save as a shapefile - that requires Map or Civil (so far as I know). This means you have plain CAD data, which uses a local, Cartesian coordinate system (ie there's an origin at 0,0 and then x/y coordinates on a flat plane). This means you'll have to address the conversion/alignment on the GIS side.
In ArcGIS, that means the Spatial Adjustment toolbar. This is georeferencing for vector data rather than raster (image) data. You'll first import the data and set the CRS to WGS84. Obviously since the units and origin and everything else are different, it will come in at the wrong place. You'll then use the tools under spatial adjustment to create link points between features in the CAD data and where they should be relative to your other layers. Then, when you run the spatial adjustment it will scale/transform/rotate/move/warp/etc. the CAD data to fit. Note this can and probably will introduce distortions, so lines that were exactly 5 meters or feet long in the CAD file may not be exactly that after adjustment. Particularly going from a planar (projected) to a ellipsoidal coordinate system.
There is a very slim chance that your CAD data is already on a projected coordinate system even if you have plain CAD. Since projected CRSs are planar, it's just a question of whether the units and origin match a known projected CRS (for instance a state plane or UTM zone). Almost if not all of them use false eastings and northings, so if your CAD data is anywhere near the origin of 0,0 it's a good sign it won't match a known system. But if the coordinates are out in the hundreds of thousands range and you can identify the projection, you would simply define the CRS as that projection when you import the CAD data. It would be reprojected on the fly in your dataframe, but to make it permanently match your other layers you'd need to use the Project tool on it (not Define Projection).