Power received by RFID tag
The definition of the aperture of the antenna is


  The aperture is defined as the area, oriented perpendicular to the direction of an incoming electromagnetic wave, which would intercept the same amount of power from that wave as is produced by the antenna receiving it.


(source)

So if you know the aperture of the antenna, you already know, by definition, the area which, when multiplied by the intensity of the electromagnetic wave, gives the power received by the antenna. 

If the antenna isn't oriented perpendicular to the incoming wave, you'll need to multiply by an additional factor to account for that. If you know the radiation pattern of the antenna, you can calculate the orientation factor from that. 

The \$\cos\theta\$ factor I used in the previous answer assumes the antenna acts more or less like an actual aperture --- that its directive gain falls off to zero when oriented parallel to the incoming wave. If your antenna is isotropic (for example), then this is a completely wrong assumption. In general you should use the actual radiation pattern of your antenna to find the directive gain for this calculation.