After looking through the sites and stack apps, I have not found a way to check my reputation at a particular date.
Is this at all possible through the User pages or API?
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After each day when you earn (or lose) reputation you'll see a line like:
-- 2010-10-08 rep +50 = 28917
So look for the date you're interested in in this output and you'll see what reputation you had on that day.