A rotating but fixed propeller sucks in air from the front. What is the cause for this acceleration of air particles? Since propeller blades act like rotating wings, my best guess is that the blades create a lower pressure zone in front of them which causes higher atmospheric pressure air to flow into this lower pressure zone. This creates the effect if the propeller would "suck in" air from the front.
A propeller imparts momentum on the air - when the blades hit the air molecules, it gives them momentum towards the back (high pressure) side; this creates a net velocity towards the rear of the propeller. Normally air molecules in the plane of the propeller have equal probability of moving forward or backwards; the propeller's action makes the situation asymmetrical. Since more air molecules move backwards, a low pressure area is created in front - and air will be pushed towards this region be the atmospheric pressure "far away".