What I'm wondering is if I can use my ‘deflect’ ability that I get from being a monk to catch and use a magic missile shot at me?
No, you can't. Magic Missile is not a Ranged Weapon Attack.
The text of the Monk ability Deflect Missiles states the following:
Starting at 3rd level, you can use your reaction to deflect or catch the missile when you are hit by a ranged weapon attack.
A Ranged Weapon Attack is an attack that is both a Ranged Attack and a Weapon Attack; Magic Missile is neither. In fact, it's not an Attack at all, since it automatically hits. As a result, Deflect Missiles does not apply to Magic Missiles.