It’s not exactly a demo, but clicking the Download Demo button on Steam’s Saints Row 4 page will get you the Saints Row 4 Inauguration Station. Or “the Saints Row 4 character creator”, if you’re feeling a bit less fancy.
The Inauguration Station will let you create and modify your Saints Row 4 protagonist ahead of the game’s launch, and get him or her ready so that you don’t have to faff around with character creation when you’d rather be acting like a president and/or shooting things. This is reportedly the full character creation tool, with everything from body size to clothing to voices, so you can customise basically everything to your liking.
Saints Row 4 itself is out on 22 August.