The Chain Pig can be used on single-speed setups but may require some modified setup and usage techniques based on the lack of derailleur, chain position relative to the frame, and chain dimensions.
For the derailleur hook and chain position, you may be able to hook the derailleur hook around the axle next to the rear cog. When trying this, make sure the Chain Pig body isn’t contacting the frame and being pushed out of alignment. Alternatively, the best solution is to remove the derailleur hook and hold the Chain Pig in place with your hand.
The next consideration is the size of your chain. Since single speed chains tend to be wider than multi-speed chains, you may find the Chain Pig runs with some extra resistance. The openings on Chain Pig body are 10mm wide and should allow most chains to pass through. The sponge may also have some issue with wider chains but can easily be removed if needed.
Lastly, you can check out the usage instructions here for additional information.