Do surface mount resistors have voltage ratings?

Yes, they have a voltage rating.

To know which size is appropriate, you have to check the datasheet because it may depend on the brand/model of the resistor.

As an example, for these resistors, 0603 is safe up to 75V, 0805 up to 150V, and 1206 up to 200V. Beware that for AC, you must check it against the peak voltage, not RMS value.

Note that, often, people use multiple small-sized resistors in series rather than a big one. Which choice is better depends on your parts stocking/purchasing policies.

They definitely have voltage ratings, which will be explicitly declared in the datasheets (yes, resistors have datasheets!). While it is possible to get arcing of the pads, exceeding the resistors voltage ratings may sooner cause breakdown of the resistive material of the resistor which can in turn cause the it to either go open circuit if you are lucky, or if you are unlucky short through.

Typically an 0603 will be in the region of 35-50V, though you can get higher ratings (e.g. 70V) if you go for more specialist resistors. 0805 is typically 60-70V, but again they do go higher with more specialist resistors.

If you are running directly across 120Vrms (i.e. not in series) you need at least a voltage rating of 180V! Why? because the peak voltage is 1.414 times higher than the RMS, and you should need some head room. For that you probably need to start looking at 1206 at a minimum (again, check datasheets) but likely larger sizes to be safe (and to be able to use cheaper/easier to find resistors).

If the resistor is in series, the voltage rating doesn't necessarily need to be quite as high - it will depend on the current through the resistor. However this is design dependent and it may still be wise to spec the resistor for the full voltage if it is somewhere in the design where there is a chance that it can be exposed to the full voltage in some unexpected condition.