Stone can absolutely be dated, especially if it was heated by fire—archaeomagnetic dating.
Archaeomagnetic dating is a method of dating iron-bearing sediments that have been superheated — for example, the clay lining of an ancient hearth.
For radiocarbon dating to be possible, the material must once have been part of a living organism. This means that things like stone, metal and pottery cannot usually be directly dated by this means unless there is some organic material embedded or left as a residue.
To establish the age of a rock or a fossil, researchers use some type of clock to determine the date it was formed. Geologists commonly use radiometric dating methods, based on the natural radioactive decay of certain elements such as potassium and carbon, as reliable clocks to date ancient events.
Geologists do not use carbon-based radiometric dating to determine the age of rocks. Carbon dating only works for objects that are younger than about 50,000 years, and most rocks of interest are older than that. ... Over time, carbon-14 decays radioactively and turns into nitrogen.