If you flew around the world in the opposite direction to the earth's rotation but flew at a very slow speed (long enough for the earth to have rotated once around) then an entire day would have passed. Thus, you could arrive back where you started earlier than you had left but on the following day. This would just be a terrible case of jet lag. If, you traveled so fast that you went all the way around the earth without it having rotated very much you could arrive back where you started just after you left. Either way, you would not have travelled back in time.

To think of it another way, imagine that you went up in a hot air balloon and floated above the earth. The fact that you are above the Earth does not affect the passage of time in any significant way. You can go any direction you want and yet the people of the Earth still age and their clocks still run. You can go wherever you want, in whatever direction you want, at whatever speed you want and their clocks will still run. No matter what you do, those clocks will run and will thus be later when you get back then they were when you left.