The meander algorithm is a combination of using mazes to allow a meandering with bresenhams line. Below you can see the actual algorithm in simplicity. Obviously you could use noise maps to created heighted terrain based on the river to make it look pretty.
Choose a starting map edge and ending map edge, acquire
the terminal points based on those edges. Usually this would be a random point on those edges. Maybe you'd want to weight it so it's predominately in the center, or you could restrict it to a certain part.
Create Bresenhams line between the terminal