@log2ex setup for summary cards happens via meta tags on the target website and there’s actually no setup on Twitter’s end. As long as the meta tags are correctly specified off-site, Twitter’s crawler will process the links included in your tweet and build the card from those meta tags.
You can of course promote regular content that includes links to sites that have been setup for summary cards through the Ads API, but there will never be an API for creating summary cards due to the fundamentals of how that type of card actually works.
Related documentation:
https://dev.twitter.com/cards/getting-started
https://dev.twitter.com/cards/types/summary