Equivalent Series Resistance of 13.56 MHz RFID Antenna
It‘s not so easy to calculate Ra, although a close approximation of Ra is the copper dc resistance Rdc of the coil. 

The reason why Ra is not exactly Rdc is that at 13.56 MHz frequency, there‘s a thing called skin effect which drives the current from copper center to the copper surface and thus increases the resistance. 

Best thing to do is to measure the resonance frequency of the coil and successively change the tuning cap C until you got a perfect driver match (usually 50 Ohms).

In general, you don‘t need to care that much about Ra in first place, because Ra merely defines the quality factor Q (or bandwidth B) of your LC resonant circuit.