Federico Viticci showed Overcast's url scheme to subscribe to new shows in his review of the app. Use the following scheme:
Viticci was also kind to provide a Launch Center Pro action and a Safari bookmarklet. From Viticci's article:
Overcast has a URL scheme to add new podcast. Using the `overcast://x-callback-url/add?url= scheme, you'll be able to subscribe to new shows in Overcast by launching the URL from other apps such as Launch Center Pro, Drafts, or Safari. Here's a Launch Center Pro action and a Safari bookmarklet to send the clipboard or current webpage to Overcast, which will parse the URL and find the associated podcast feed. Overcast's URL scheme also supports x-callback-url, which is good news for iOS automation workflows.
Check the article on MacStories for more details.