Theoretically a star could orbit a planet, but the star would be very tiny and the planet would be very massive for it to happen. This is unlikely to exist.
Technically, jupiter does NOT orbit our sun, it is so massive that the sun and jupiter both orbit around a central point called a barycenter which is 0.07 solar radius above the surface of the sun.
The rest of the planets also have a barycenter with the sun but they are all inside the sun.
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