Stack Exchange has special social network profiles for each site (like our @StackCogSci on Twitter), but they also have "parent" accounts for the whole SE network, and they have a process for advertising questions on those accounts.
Basically how this would work is we'd find Good, answered, questions that give a good, understandable impression of our site and content, and subit the question via this official form. Since these would be shared with all of the Stack Exchange network's followers, try and pick something relatable to a general audience with a good answer rooted in format science. We want to give the impression that there's real, relatable questions out there we're answering with authoritative answers and sources.
Note that you can share Cog Sci's content at any time with your friends on Twitter/Facebook/ect. Try and pick targeted, easily relatable content. If you've got friends/colleagues that are researchers, throw them one of our answered research level questions.
