You cannot use a voltage divider to power a load, as you have found out!
Why? When you attach a load to the divider, the load draws current. This current flows through the top resistor and causes a voltage drop.
You say that you have around 2.5V when the Arduino is connected. This means that the voltage drop across the top resistor is 12-2.5 = 9.5V
Ohms law shows that:
9.5V / 2200 Ohms = 4.3mA
This is the combined current that is drawn by the Arduino and the bottom resistor.
Without the Arduino connected we have:
12V / (3300 + 2200) Ohms = 2.18mA
2.18mA x 3300 Ohms = 7.2V
This is the 7.2V you were expecting
Hopefully this makes sense