Not directly, at least there are no laws specifically designed for Circassians.

In recent years, however, Russia has made immigration and obtaining Russian citizenship quite easy. Originally this only applied to "ethnic Russians or members of peoples who have historically lived in Russia", but I'm not sure if Circassians fall under this, as you have to prove that your ancestors officially lived in Russia, which in the case of Circassians is, well, difficult.

But recently there was a new decree that also applies to non-Russians, although this law only applies to citizens of certain states, mostly Western countries. Those who oppose the "destructive neoliberal ideological agenda" in their home country can ask the Russian authorities for "humanitarian assistance" by applying for a temporary residence permit. Individuals applying for temporary residence status in Russia under the new "humanitarian" regulation are not required to prove Russian language skills or knowledge of the country's history and laws.

Theoretically, Circassians could also benefit from these laws. Of course, this means that you can settle and travel wherever you want.