Vaccines are being administered at the Arlington Airport. You may book your appointments at this link

Scroll down and select Arlington Airport as the sight and answer the questions. You will be send an email confirmation of your appointment time. When you show up, show the email (can be shown on your phone) and ID.

The entire process is very well designed and runs very smoothly without ever leaving your vehicle. Once the vaccine is administered, you will drive up to another line and will be released 15 minutes afterwards.