How to capture smart phone's mac address using Arduino?

I tend to build something which can recognize my phone's mac address for being able to light an LED. It will work like this, if i come across the wifi zone (which will be transmitted by the device i tend to build), it will capture my phone's mac address and check if it's my mac or not, if it is then the device will turn the LED on. Any idea, how will i get that done ?

You will probably find you need something like an ESP8266 board to do that kind of layer 2 work. If you flash your ESP8266 to the nodeMCU firmware you may well find you dont need the arduino at all. Most arduino projects along these lines tend to use bluetooth rather than wifi because its cheaper and easier.

Be warned its fairly trivial to capture and spoof a wifi MAC address so its OK to use to turn on your lights when you get home but I wouldn't use it to open your door.

The ESP8266 doesn't have that functionality in either the Lua firmware or the Arduino core. You could extend those firmwares to add an API to do ARPs, but if you knew how to do that you probably wouldn't be here asking ;)

The Yun can do it pretty easily, of course.