Driftsort an array

Ruby, 33

->a{a.any?{a.sort==a.rotate!}&&a}

a.any? fires up to once for each element in the array, except it stops (and returns true) as soon as the array has been mutated into a sorted state. If this happens, we return the mutated array. Otherwise we return the false value that any? returns.

Python 2, 51 bytes

lambda l:sorted(l)*(map(cmp,l[-1:]+l,l).count(1)<3)

Doesn't bother rotating. Instead, sorts the list, then sees if the original is drift-sortable by checking if there's at most one decrease among consecutive elements of the cyclified list. The count is <3 because map pads the shorter list with None at the end, adding a fake decrease.

Pyth, 9 bytes

*SQ}SQ.:+

Explanation:

           - Q = eval(input())
         + -    Q+Q
       .:  -   sublists(^)
   }       -  V in ^
    SQ     -   sorted(Q)
*SQ        - ^ * sorted(Q) (return sorted(Q) if ^ True)

Try it here!

Or use a test suite!