Does a police officer have to read your Miranda rights before placing you into a police car for a DUI

Not necessarily.  Your Miranda rights need only be given if you are taken into custody and then questioned.  If you are questioned before an arrest, this is allowed.  If you are questioned after your arrest, then the arrest may be unlawful.  Asking questions relating to your booking, for example, is permitted.  So if you are asked your name and address, those type questions do not implicate your Miranda rights.  However, if arrested and then asked questions about the alleged crime, a Miranda warning must be given.  If it is not, then anything that you say after that point may not later be used against you.