Can I put 2013 cts rims on my 2004 dhs?

Those tires would be 1.5 inches too small in overall diameter.

As far as I can tell, offset requirement is the same between the two cars, meaning the adapters would make the wheels stick too far out. But don't quote me on that, I'm going off of offset listing I found with a Google search.

Someone will have to confirm the offset for the CTS rims. The Devilles original rims are +40. Most high positive offset rims will work.

If the rims fit, you'll need tires.