All of the official SE Twitter accounts were controlled by us. That particular one actually belonged to the original Economics site which was closed in 2012 around the time of the last tweet from the account.
We stopped creating Twitter accounts for new sites some time ago - it's just not worthwhile to integrate them anymore given the low engagement and hassle of getting them unblocked with Twitter. It's unlikely we'd ever re-activate the existing one, as it'd probably end up getting blocked by Twitter if it started up again and that's exactly the kind of thing we don't want to deal with,
but I can bounce the idea off some people and see if it's in the cards, y'know, since it does already exist.
So apparently this has also come up before, and the simple answer is you should feel free to create and operate your own Twitter account, but we cannot hand over the existing one that we operated. If you do go on to create your own Twitter account for the site, let us know and we will deactivate the existing one to prevent any confusion. Please make sure you follow the advice in the linked post as well.