Here is one way:

    movingMapCircular[f_, l_List] := MapThread[f@* List, {l, RotateLeft[l]}];

For example:

    movingMapCircular[f, {1, 2, 3, 4}]

    (* {f[{1, 2}], f[{2, 3}], f[{3, 4}], f[{4, 1}]} *)