Can I connect an Android smartphone to an Arduino Uno?
Not directly like you think. The 4 wires are for a USB interface, which the atmega328P on the Arduino Uno does not support. There are Arduino boards that have a USB interface AFAIK, but this won't be a trivial thing to do. Or you could add a USB to SPI breakout board, but that probably won't support high speed USB.

Another option is to use a BLE enable Arduino module/board, and connect remotely. But again, you will have a decent bit of programming to do on the phone and the Arduino.