Is there any way to determine power rating of a potentiometer?

Hmm... how big is it? Most potentiometers I have found are rated for 1/2W or 1W. A general rule of thumb though is that you shouldn't be putting much power through it anyway - it should only be controlling a small signal.

Please note that the power rating of a potentiometer is for the entire end-to-end resistance. If you use (as is typical) a fraction of the potentiometer's end-to-end resistance, the power is reduced accordingly. The easiest way to think about it is that there is a maximum current through the pot. If you have a 1W 100 ohm potentiometer, the max. current is 100mA (full voltage = 10V); if you are using only 27 ohms of the potentiometer then the max. current is still 100mA and your effective max. power is 0.27W.

That particular pot is similar to those used in old-time hand-held transistor radios. My recollection is that thost are good for perhaps 200 mW at most.

You can often estimate how much power any particular potentiometer can handle based on the physical size and the material that the resistive track is made from. Although experience helps you arrive at an estimate, you can also simply look at a catalog of pots and compare what is in the catalog to what you have. Digikey or Mouser have great on-line catalogs, for example.

Resistive track material is important. You can usually tell if the track is wire-wound by simply rotating the shaft and feeling for the telltale lumps that occur as the wiper moves over the track. If the rotation is smooth, the track is most likely either carbon or carbon film.