Also, R2-D2 is a droid Jedi.
Forget light sabers and force pushes, the power of a Jedi is to set their mind to something and then succeed at it. Do, or do not - there is no try. That is the true power of a Jedi.
Think of Anakin leaping from flying ship to flying ship, high in the sky of Coruscant, never once slipping off. Or just swinging your light saber and reflecting each shot from a blaster back at your enemy. Think about going alone, deep into the Death Star to shut down the tractor beam so that the Falcon could escape.
And in this way, R2-D2 is clearly a Jedi. Even in his introduction in Phantom Menace, he succeeds in repairing Padme's ship, while all the other astromech droids were blown away. On Bespin he unleashes a smoke screen and casually rolls through it, laser beams zooming by all around him, but none ever hit him. And oh btw, he discovers that the Falcon's hyperdrive has been sabotaged. On Tatooine he just takes off into the desert in search of Ben, and finds him.
Like a true Jedi, I can't think of a single thing that R2-D2 did - not tried, DID - and actually failed at.