12V Signal -> Relay -> Voltage Regulator -> Arduino mega analogue input. Will this work?
Don't bother with the 7805 - without input and output capacitors this could prove problematic and, at the very least will be "slow" in responding to the 12V input.

Just use a resistor and 4.3V zener diode like this: -







simulate this circuit &ndash; Schematic created using CircuitLab

You don't need to worry about glitches either because the relay coil is isolated from the Arduino by the relay contacts.