Yes you can. Assuming you are using the default 5V analog reference, you can get the ADC to read the internal bandgap voltage reference. Looking at the code for analogRead, I believe that on the atmega328-based boards, you can so this by calling analogRead(28). The reading you get will be 1024 * (Vbg/Vcc) where Vbg is a fixed voltage for any particular chip, nominally 1.1V but possibly anywhere between 1.0V and 1.2V. Since Vbg is fixed, you can calculate Vcc from the reading.
Thank you. It is interesting to know that the "pin" 28 is for the internal bandgap. Could you tell how to find the code for analogRead()?