@THNXbot, thanks for the clarification. You might be able to get Tweet IDs with the Ads API, but I’m not sure. It may not be possible. It definitely cannot be accomplished with the public APIs.
Metrics can be found at analytics.twitter.com. If you have implemented the twitter:site meta tag, you can get the number of impressions your card has generated.
You could try using the search API using your URL as a query, but it only goes back 10 days and is not guaranteed for completeness.
If your business model supports it, you can look into Gnip Historical Powertrack, which is a paid product. You could get every single Tweet with specific URL or keyword.
Lastly, I would recommend using the filter stream using your card URL as a track parameter. You will get Tweet objects in real-time as they are Tweeted. This will work for you as long as your URLs account for 1% or less of all Twitter traffic.
