Not in this century, it isn't.
Just as we use the apostrophe to show possession in the phrase "Mary's head."
There are some pronouns that use the apostrophe for possession:
one's, everyone's, nobody's
But we do not do so with the personal pronouns. The following would all be considered incorrect as possessives:
*me's, *us's, *you's, *him's, *her's, *it's, *them's
Instead each of these have their own possessive pronoun that can be used independently:
mine, ours, yours, his, hers, its, theirs.
And that can be used with a noun:
my, our, your, his, her, its, their.
(Note that his and its are in both sets).
Historically we would once have found cases of her's, it's and their's here ("Their's not to reason why, Their's not to make reply, Their's but to do and die.") but that was for a brief period in the 19th century and wasn't that common even then. Such cases are long gone.
The only use of it's now generally considered is as a contraction of "it is".
So if you find the cases where Alfred, Lord Tennyson or Abraham Lincoln made use of it such apostrophes, they weren't incorrect, but unless an excitable chap turns up in a materialising police box and asks if you'd want to go on an adventure you shouldn't do so yourself.