Not quite.
Or at least, there is at any instant, but that point moves around (very slowly and over short distances), so you would have to follow it.
The Earth doesn’t spin perfectly, it wobbles slightly. There are three main kinds of wobble; an annual wobble, a thing called the Chandler wobble (that repeats every ~435 days), and a gradual drift.
This polar drift used to be heading Westwards (and shifted about 20m during the 20th century), but since 2000 seems to have changed direction, possibly related to global warming shifting water mass around.
But yes – ignoring that, there are two points – at the poles – were you could stand and you’d spin around once every day.
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