I am making a light fixture into a swag light fixture as I have not outlet box to use. The new light fixture has a ground wire but none of the swag kits tell me what I should do about the ground wire.

Connect to the ground terminal on a 3 prong plug.

The ground wire should be routed with the hot and neutral throw the chain, and then go into your junction box, it should be attached to your ground wire in the j-box

I have not outlet box to use.

All connections must be made in a box. Connections to existing fixture must have been made in the fixture itself. Install an "Old work" box then make connections to swag light in box. If house wiring does not have a ground then leave ground to swag unconnected.

If I understand you correctly, you want to put a lamp cord and plug on a fixture which was designed for installation on a ceiling box... is that correct? If so, you will not use the ground wire for this installation. Make sure you observe polarity with the lamp cord.