The turtle is a symbol of 1) nature and its resiliency and 2) the spirit of the migrant family.
The turtle in Chapter 3 symbolizes Nature’s struggle and the will to survive. It characterizes the will to survive of the Joads and “the people.”
In this chapter, the turtle's determination and drive are expressed in clear terms. Though we cannot know where the turtle is going, the turtle knows and refuses to be stopped. When attacked by the red ant, the turtle goes on. When hit by the car, the turtle again continues on.
This is the spirit of necessity and the spirit of survival that also animates the migrant families as they move west looking for new opportunities.