How old should a child be when they learn to play the guitar?

Unfortunately, there isn’t a simple answer to this question. You shouldn’t keep a child from learning an instrument solely because you feel they are too young, but you also don’t want to push lessons on them in hopes they will learn early.
To know if your child is ready to learn the guitar, give them an opportunity to try one out and get a feel for their interest level. Regardless of whether your child is 4 or 13, they have the potential to be a great guitarist.