Yes, Raspberry PI and Beagle Bone Black. Its a bit more work because it is something that is not as refined as the rest of the LinuxCNC family. But it is a downloadable install now.
If an Arduino Uno can run the LinuxCNC core (aka Grbl) then pretty much anything could potentially run it.
The Sieg X3 conversion in my shop was assembled in 2010 using a 2 core Atom machine with 4 GB RAM. I still use it 3 to 4 times a week.
That is much less than most RPis.