Can an iphone/android cell phone communicate with RFID?
RFID is typically Tag sending a message, usually just an ID number, to a Device, which reads it. You want the other way around, which is not how RFID is used. NFC can be used for two way transmission (Like touching the back of two NFC phones to pass data), but it's also mainly used as an ID system, Tag to Device.

You can have a NFC device act as a tag, which your circuit would then scan for. For this you need a NFC reader as well as your microcontroller.

Bluetooth, and Bluetooth LE are the way to go.