No, you can't. Instagram has not implemented a feature that enables users to see who has taken screenshots of their stories. This is a common concern among users, especially those who share personal or exclusive content on their stories. But currently, all you can see are the views and some basic interactions on your story, not screenshotting activities. Some people might think this is a privacy issue from the perspective of the story creator, but it also protects the privacy of those viewing the story in a way.
Instagram doesn't offer a native way to find out if someone has screenshot your story. It's important to note that Instagram focuses more on the general engagement metrics like views, likes, and comments for stories. The absence of a screenshot - detection feature might be to keep the user experience simple and not overly intrusive. There have been rumors of Instagram considering adding such a feature in the future, but for now, we can't know if someone screenshots our stories.