Why does the vortex created by wing affects its own angle of attack?
The wingtip vortices create both upwash and downwash; The downwash lies within the wingspan and affects the wing angle of attack while the upwash region lies outside the wingspan and can be utilized by another aircraft (or bird) flying behind and above the wing.

The flow induced by the downwash reduces the effective angle of attack of the (finite) wing and causes the induced drag.

See if this image clarifies your doubt.



Source: aerospaceweb.org



Consider the upwash before the wing and downwash after the wing (section).



Source: theairlinepilots.com

As it can be seen, the airflow in front of the wing is slightly directed upwards by the upwash. Now, the angle the wing makes with the horizontal datum (i.e. relative airflow) is the same. 

However, the airflow is slightly turned upwards and the wing sees the air coming at it at a different angle compared to the relative airflow. As a result, the effective angle of attack (defined as the angle of attack that lies between the chord of an airfoil and the effective airflow) is reduced, so that the relative and effective airflow looks something like this:



Source: theairlinepilots.com

This difference between the relative and effective airflows is what that causes the induced drag.



Source: theairlinepilots.com