If you could travel at the speed of light on Earth and remain stationary relative to the Earth's surface, you would essentially be in orbit around the Earth at an altitude of approximately 35,786 kilometers (22,236 miles). At this distance, you would be in what's known as a geostationary orbit.
The circumference of the Earth at the equator is about 40,075 kilometers (24,901 miles). If you were in a geostationary orbit, you would complete one orbit around the Earth in approximately 24 hours, which is the same amount of time it takes for the Earth to complete one rotation on its axis.
Therefore, at the speed of light, it would take you approximately 24 hours to complete one orbit around the Earth.