Creating a user account on a Stack Exchange site results in Stack Exchange creating a generic profile page that contains statistics and layout and other standard gubbins that is common to all Stack Exchange profile pages. That standard gubbins includes the placeholder text, "Apparently, this user prefers to keep an air of mystery about them."
Users may optionally contribute additional content to their profile page(s), including via the "About me" profile page field. If a user does contribute content via the "About me" profile page field, then that content replaces the placeholder text, "Apparently, this user prefers to keep an air of mystery about them."
Looking at this from a different angle: for "About me" content to be published, that content must be contributed by some entity. Only Stack Exchange, Inc., employees and the user should have the ability to edit the "About me" profile page field. In the case of legitimate users' profiles, Stack Exchange, Inc., employees do not normally edit the contents of that field. So, barring vandalism by someone who has attacked the integrity of the website or stolen the user's credentials, the only remaining entity who could possibly contribute the "About me" content is the user.
Therefore, the "About me" profile page field is user-contributed content: i.e. it comprises a "user contribution" to the Stack Exchange network.
Such user contributions enrich Stack Exchange and make it more interesting. In some cases, they may even make it more useful.
Now, to answer your question: at the bottom of every profile page on the Stack Exchange network, there appears the text, "user contributions licensed under cc by-sa 3.0".
Therefore, the "About me" portion of Stack Exchange user profile pages is indeed licensed under CC BY-SA 3.0.
N.B. The Stack Exchange Terms of Service lead to the same conclusion, albeit by a slightly different route. Whereas the Stack Exchange profile page footers talk of "user contributions", the Stack Exchange Terms of Service talk of "Subscriber Content". In the context of Stack Exchange, these are effectively equivalent terms. The Terms of Service define "Subscriber Content" as "Content posted by Subscriber". "About me" content posted by a Subscriber (i.e. logged-in user) of a Stack Exchange website is therefore, obviously, a kind of Subscriber Content.
As for the license applied to Subscriber Content, this is what the Terms of Service say:
From time to time, Stack Exchange may make available compilations of
all the Subscriber Content on the Network (the “Creative Commons Data
Dump”). The Creative Commons Data Dump is licensed under the Creative
Commons Attribution Share Alike license.
You agree that all Subscriber Content that You contribute to the
Network is perpetually and irrevocably licensed to Stack Exchange
under the Creative Commons Attribution Share Alike license.
So, from this perspective too, we can conclude that the "About me" portion of Stack Exchange user profile pages is indeed licensed under CC BY-SA 3.0.