A commenter faults my quoting Blackstone's "The falsehood of it may aggravate it's guilt, and enhance it's punishment":
"it's" = "its" in standard English, and also in the original, according to Google Books.
Many people do take the view that modern standard English is Good Old English, and that usages that are seen as erroneous today are some modern inventions. (I don't know if that's the commenter's general view, but I have heard many people express such arguments.) But while "it's" as a possessive of "it" is indeed not standard in edited English prose today -- perhaps it will be one day, but to my knowledge it's not so right now -- it appears to have been standard in the past. The Blackstone quote is one example, but the OED offers several others, including from Shakespeare; the latest such source the OED gives is 1802, which suggests that the usage was pretty standard at least until then.
But what about the commenter's assertion that the original actually says "its"? The trouble is that the source the commenter cites is actually not the original. I looked up the original 1769 Oxford edition in Eighteenth Century Collections Online (the Commentaries were published starting with 1765, but volume 4 has a publication date of 1769), and it says "it's." So don't assume that what would be generally seen as an error today would also have been seen as an error in the 1760s, and don't let this assumption fool you into treating early 1900s editions as authoritative about the "original" spelling.