What will AC voltmeter show when connected to a DC source of 120V
If you are using a scope with AC coupling, then it will read zero because it isolates DC, but if the AC coupling is off, then it will give you the true DC value.
If you are however talking about "AC Voltmeters" which are quite uncommon since one can easily use DC Voltmeters to read AC RMS; the ones I have dealt with use a rectifier, and holds to voltage across an RC channel and then reads the voltage as DC. The rectification can be done using a single diode or a full bridge rectifier, I found this circuit online:
Clearly this circuit will read DC values same as AC values, so long as the DC voltage is positive, if a full bridge rectifier was used instead of the single diode, then the absolute value of the voltage would be read.
Theoretically it should show the correct voltage of the source, because average, root mean square and maximum of the constant voltage is just that voltage itself. What else the AC voltmeter could be supposed to indicate?
However this depends. For instance, if the single diode is used to rectify the AC, the device still can be calibrated to indicate the value for AC properly but will show zero on one polarity. An old, analog (electromagnetic) indicator will likely display double voltage for another polarity.
Are you asking the question because you only have some kind of a meter that just measures AC? Why would you want to use it? You can buy a DMM with a 1000 VDC range for $6.79, and it will also measure AC voltage and resistance in several ranges.
You must know this: you have an internet connection, so it must be a question to settle a bet or idle curiosity. The answers all answer the question to some extent: "It all depends." What meter?