It is not a complete sentence because it has no subject; it doesn't say who or what is banging on the door.
Mary is banging on the door.
They are banging on the door.
The branches are banging on the door.
Who is banging on the door?
The grammar police are banging on the door.
Or you can make the 'banging on the door' the subject of a sentence, but it will need its own verb:
That banging on the door is annoying.
Banging on the door broke the window.