Can my 13-year-old son make his own choice as to where he would like to live?
No. Unless your child is legally emancipated from you, then he cannot leave your home without your permission. If he leaves your home without your consent, then you may contact the authorities to report a runaway. The police will help you locate and return him into your custody.
If this is in regard to a child custody dispute you have with your child’s father, then most states will not permit a minor child to choose which parent they would like to with. However, depending on the family law provisions of your state, if he is 12-years-old or older, the judge may hear his testimony about which parent he would prefer to reside with. Note, the judge is not obligated to place him in his preferred home.