Short answer: Yes you can
Android provides BluetoothSocket that :
It is also known as the Serial Port Profile (SPP)
This class offers you two streams (one for reading and one for writing) that you can use to read/write bytes.
Example of opening a socket:
BluetoothDevice mBtDevice;
BluetoothSocket mBtSocket;
mBtSocket = mBtDevice.createRfcommSocketToServiceRecord(MY_UUID);
mBtSocket.connect();
Of course in order to do that the other device must be paired with your phone. After they are paired you can select your device from the list of paired devices provided to you by:
BluetoothAdapter mBtAdapter = BluetoothAdapter.getDefaultAdapter();
Set<BluetoothDevice> pairedDevices = mBtAdapter.getBondedDevices();