Lexus Stagg, 26, is charged with with criminally negligent homicide in the death of her son on 11 June.
A surveillance video from a block of flats in Houston shows Ms Stagg getting into a Lincoln Navigator.
As she reverses the car, her three young children can be seen running after it.
The video then shows Ms Stagg driving forwards again, as the children try to run away from the vehicle.
Two children moved out of the way, but the three-year-old was caught under a tyre, police said.
Harris County district attorney Kim Ogg said: “Cars aren’t toys, and playing chicken with your kids isn’t a game.”
Ms Stagg was taken to Harris County jail, but was no longer being held on Saturday.
It is unclear whether she has a lawyer to speak on her behalf.