Yes eating some sauerkraut can help get rid of constipation and get your bowels moving.
Sauerkraut contains probiotic bacteria which helps your bowels get moving so that your stools can be loosened up and then you should begin pooping.
I find that eating a bowl or two of sauerkraut when I'm constipated helps me poop within a few hours after eating it so it does work.
But if your constipation is more severe you might need to take laxatives or drink some prune juice, drink more water, eat prunes, take some castor oil etc.
The bacteria in the sauerkraut is able to help break down the food much better in your stomach and intestines which helps your stool become softer and makes it easier to poop.