It seems that svg-file with the logo is available here: https://cdn.sstatic.net/Sites/math/Img/sprites.svg?v=fa2277060fb6 <br>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:

[![sprites][1]][1]

You can also find the logo in these posts (although not in svg format): [Design Ideas for Mathematics Site](https://math.meta.stackexchange.com/q/963) and [Do those red cubes aligned circulary next to MATHEMATICS have any mathematical significance?](https://math.meta.stackexchange.com/q/13398)

<hr>

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?](https://meta.stackexchange.com/q/22117), SO page with [logos](https://stackoverflow.com/company/logos) and [Guidelines for the Use of the Stack Exchange, Inc. Trademarks](https://math.stackexchange.com/q/trademark-guidance).

Since you have mentioned that you want to use this to link to your account, the fact that [flair](https://meta.stackexchange.com/tags/flair/info) 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.)

 [1]: https://i.sstatic.net/EkvDs.png