It seems that svg-file with the logo is available here: https://cdn.sstatic.net/Sites/math/Img/sprites.svg?v=fa2277060fb6
I got the link after choosing "Inspect" and "Sources" in Google Chrome, while viewing the site.
It seems that svg format is not supported as a format which can be used in posts. So here is at least a screenshot showing the content of the svg file:
You can also find the logo in these posts (although not in svg format): Design Ideas for Mathematics Site and Do those red cubes aligned circulary next to MATHEMATICS have any mathematical significance?
As mentioned in the comment, you should keep in mind copyright/trademark issues. See also: What are the rules on using the Stack Overflow logo?, SO page with logos and Guidelines for the Use of the Stack Exchange, Inc. Trademarks.
Since you have mentioned that you want to use this to link to your account, the fact that flair can be used for this purpose should be mentioned.
(Both these issues were raised in the comments by quid - I think they are important enough to be mentioned in an answer.)