Controlling RFID with arduino

I'll make a project that consists of a bracelet that has implemented RFID, and that the slope it to a cabinet door she locks the bracelet. Then the door so the cabinet can be opened with this bracelet. My questio is: I can control the bracelet with the arduino, in other words, the RFID reader can be worked in arduino?

Yes.

https://www.google.com/search?q=rfid+arduino&oq=rfid+arduino&aqs=chrome..69i57j0l2j69i60j0l2.2896j0j7&sourceid=chrome&es_sm=93&ie=UTF-8

In fact, you can even build your own RFID interface:

http://playground.arduino.cc/Main/DIYRFIDReader