I am assuming you have an RFID reader that has a Wiegand output. If so it is very easy to read. Simply monitor the two inputs to the arduino and add 0 or a 1 to the number you are building up depending on which one you see pulse.
You need to know how many Weagand bits you are expecting.
Another way would be use each Wiegand output to trigger a separate interrupt. Then let the interrupt service routine just append a zero or 1 and increment a “bytes received” variable. Then in the main loop when the correct number of bits are in do the parity checking and pass the number on to your Ethernet routines.