Secondary Effect

 An Aeroplane causes Roll when the rudder is applied.

This is mainly due to the lift generated by the wings. There are two ways lift can be generated. Angle of Attack and the Wing Camber (the general curviature of the wing).
Angle of Attack creates lift by using Newton's 3rd Law(every action has an equal and opposite reaction). The relative airflow that hits the wing from below deflects the air down making the airplane go up.
The wing camber creates lift by the principle of a person called Benoulli. The principle states: the faster the speed, the higher the pressure.
Looking at a wing, it is usuall flat bottom with a curved top. This is for the reason that when an airplane travles through the air, the air travelling through the top of the wing has to travel faster than the air at the bottom as it has a greater distance to travel. This also means that since the air on top is travelling faster, it has higher pressure. Low pressure always goes to High Pressure (also the same in meteorology) and the same happens with aircraft. The air under the wing wants to go to the air on top taking the wing with it.

The wing camber is what we are interested in.
When the rudder is applied, for this example we will take a pilot using left rudder, the aircraft yaw's to the left. (Newton's 3rd law means that the air is deflected to the left near the tail pushing the tail to the right and the nose to the left).

With the aircraft yawling to the left,  The right wing travles in a large radius around the outside. This means that the right wing is travelling faster than the left wing (take an athletes running oval for example. The people on the insides of the oval start before the people on the outside as they have less distance to run).
Since the right wing is travelling a larger distance, the airspeed on that wing increases. Since one way lift is created is through the Camber, the right wing generates more lift in comparison the the left wing causing the right wing to raise which gives you bank.