In a sense it really has four "states", since the ant remembers which direction it had previously moved. That's implicit in the clockwise/counterclockwise rule.
I would say there are 10 states. Any square can be empty or have an ant, and if the ant is there its direction is known. That gives 5 states of ant presence and direction, and since a square has 2 color states, that's 10 total states.
I'm counting "states" as the term's used in (tape) Turing machines, where you distinguish the internal states of the finite automaton (tape head) from the memory states of the unbounded tape (symbols or colors). So this ant would be analogous to a 4-state, 2-color Turing machine. The ant has four possible states; each cell of the grid has two.