Can an employer obtain my driving record without my consent?

Actually, no a private sector employer cannot obtain your driving record without your consent. Typically DMV records are private. Only the licensed driver and /or governmental agencies and/or public sector employers have the absolute right to see them.  However, an employee may sign a waiver giving their employer the right to view their DMV record. What the employee needs to do is to check the employee handbook and/or check with HR as to this. Also, if there was an applicable employment contract or union agreement that would control.