I think a business card slid down the side of my car window and is stuck down there, can I get it out?

Doors come apart to allow working on the window and lock mechanisms. Basically all the soft parts on the interior can be peeled open. If you don’t want to do that, I would forget it. Or have a pro do it. Without experience and the right tools, it’s hard to put it back together well.

There’s bound to be little rubber plugs in the bottom of the door, to allow for water to exit (or so I believe).
If they are present (or any other hole you can find in your door) you can have a peek with a flashlight to ensure it is there or not.
If it is, you have a new challenge at your hands.
I would want to try my luck at it, with the use of glue stick and thread, or small tweezers, or a hair dryer (to reposition it).
I would have a field day.

Or ask the person or business for a new card.

If the door and window function fine, I wouldn’t worry about it at all.

It’s not worth the trouble or expense. If you ever have to have work done inside the door, like if the window doesn’t work or falls out of it’s tracks/mechanics, then have the technician retrieve it for you.