The folks at Adafruit have shared many fun DIY electronics projects in the past. In one of their latest posts, they show how you can build your own phone with an Arduino and Adafruit FONA shield. This is a touchscreen phone that can program itself. Adafruit’s library let you customize your phone and extend its capabilities.
You are going to need an Adafruit FONA 800 shield, a TFT shield with resistance touch, a SIM card, a 1200 mAh battery, and a few other parts to get started. All the parts and instructions are available on adafruit.com.