Dig into the twitter referral traffic on Google Analytics to find the individual tweets using Google search.
1. In Google Analytics, go to the Acquisition -> All Traffic -> Referrals report. If you are getting traffic from links on twitter, you will see a source for t.co. This is the twitter link shortener.
2. Click on t.co to drill down to the referral path details. You will see data that doesn't seem very helpful.
3. To translate these referrals into the actual tweet, go to the google search bar and search for t.co/"string" where "string" is the referral path from your report.
For my example, I searched for t.co/byaGHN1QPs. This will find the tweet in which this link shortener was used.
4. You cannot search for this referral within Twitter itself. You will most likely get "No results".
You can download all your tweets from Twitter Analytics. When you do this, the tweet data will have your shortened URL, such as t.co/byaGHN1QPs. You can use this data along with the Google Analytics referral report to create lookups in Excel.