Try it online!
(If the input strictly has to be whitespace-separated, add two bytes to prepend
ṇ₁, but note that the input still has to be quoted. Brachylog does not have any sort of direct access to stdin.)
Takes input as a list of two strings, and outputs through the output variable. The actual logic is all in the first six bytes, which succeed if the elements of the input are rotations of each other, and fail if they are not:
ᵐ Both strings in the input
~c₂ can be split into two pieces each
↔ᵈ such that one string's two chunks are the other's swapped.
↔ᵈ could just as well be
oᵛ which is what it was originally before I decided that
↔ᵈ is more to the point.)
Although it would be possible to brute force rotating one of them until it matches, the number of rotations would need to be explicitly bounded, and on top of that just the effort required to separate out the two elements of the input list would be fairly costly. Since it's very easy to brute force partitions in Brachylog, the fact that a rotation is just as much taking one chunk off one end and moving it to the other as it is doing that to single characters however many times saves a lot of bytes.
With very flexible I/O, this could be as short as 5 bytes, taking one string through the input variable and the other through the output variable: