Many sites have the option for their user to add a signature to their posts. Does Stack Exchange happen to offer such a feature?
No. Signatures are actively discouraged in Stack Exchange; see the relevant meta discussion here
In general, taglines and signatures are strongly discouraged, and are likely to be edited out. We don't want to clutter up the questions page with a lot of redundant signature blocks and taglines and so forth.
Can I use a signature or tagline?
Please don't use signatures or taglines in your posts. Every post you make is already "signed" with your standard user card, which links directly back to your user page. Your user page belongs to you — fill it with interesting information about your interests, cool stuff you've worked on, or whatever else you like!
-- Jeff Atwood (StackExchange founder)