The top speed of a cheetah is 75mph.
The circumference of the earth at the equator is 24,901.55 miles.
If a cheetah could run at top speed for the entire journey it would take 322 hours (14 days) for it to circle the globe at the equator.
However, a cheetah can only run at 75mph for short bursts and would have to swim most of the way. Cheetah's can swim, but to this researcher, it is unknown how fast.
There is also the issue of sleep, eating, hygiene, stamina, etc.
So, for estimation purposes, let's imagine that the cheetah's food is provided, it doesn't have to swim, it sleeps half the day, and its casual jogging pace is 10mph. Given these assumptions, it would take 2490 hours / 12 running hours per day = 208 days for it to circle the globe at the equator.