Can I be charged for theft that someone says I did but I didn't do?

Yes. If a witness has reported to police that you committed a theft, then the police may investigate. If the police conclude that there exists probable cause to believe that you committed a theft, then you may be charged with the crime. If you end up charged with a crime, you'll need a criminal defense lawyer to represent you. It would be in your interests to retain that attorney right away, before you're charged if possible, to work some damage control.