Is it illegal to drive around with your tank full of air? 
Yes it is legal. Perfectly legal.
Every semi-truck on the road has air brakes. Air brakes use pressurized air in a reservoir for use. As long as DOT approved parts are used, the system is deemed safe for use. Try to use an ASME or SAE J-10 certified tank with your application, as well as DOT approved airlines, and you’re good to go.