Few things to say before going into details:
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Typical servos don't "spin", they wiggle from side to side. So if you really do mean spin, like a wheel, make sure you get what's called a "continuous rotation" servo. (edit... as mentioned by previous poster)
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Do you need this to happen at a particular time of day, like 5 past 3 every afternoon? If so you will need to get either an RTC (Real time clock) or be online to internet time.
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If you are just thinking of 24 hours since last time, you could use the internal timer of an Arduino but you will need to look at the accuracy. You'll also need to be aware that the time starts over if Arduino loses power...