Yes, you can! This is a field that will be disabled in your Configuration by default, but it can easily be enabled by someone with Configuration permissions.
You'll find this field in Configuration in General Shelter > Intake and Outcome > Outcome Forms > Adoption.
If a Driver's License # is collected during an Outcome, it will be available in both a Custom Events Report on Outcomes as well as a Custom Event Report on Outcomes Not Counted Towards Live Outcome Numbers as a customizable column: