Twitter’s search will let you find almost* all the tweets that contain a particular link. You can just plug in part of the link into search (desktop Twitter‘s best for this). To view all the tweets choose ‘live’ from the options and scroll down to go further into the past.
What have your friends said about this link?
If you want to see what people you follow have tweeted about this link you can restrict the search just to them. This can be useful if you click on a link earlier in the day, forget who sent it but want to acknowledge them in a tweet you subsequently send – you can work out from whom you saw the tweet.
A note on how to search for a link – try different bits of the address
Twitter’s search can be a bit mercurial – or, I haven’t worked out exactly what’s going on yet. Sometimes putting the entire link in yields nothing… sometimes it yields something. I generally select a bit of the link and choose a bit that’s likely to winnow out irrelevant tweets.
A note on the appearance of the link
Twitter does not distinguish among modified (shortened) links that point to the same web page, so searching will bring up a variety of different-links all going to the same place.
Example: here’s an address: http://www.theguardian.com/healthcare-network/views-from-the-nhs-frontline/2015/jul/13/wasting-gps-time-no-i-cant-prescribe-you-new-shoes and if you search for it on Twitter you’ll get these results which include these shortened versions of the URL which all point to the same page
If you want to share a link without having it show up in searches try something like donotlink.com (effectively it ‘cloaks’ the link by pointing to an intermediate site first).
Saving time when searching again
If you’ve just searched for apples and bananas you’ll first see all the Top tweets and then have to click ‘Live‘ to see all of them. If you decide you want to search for apples and pears you can avoid this two-step process by editing the search-result-link in the address bar (desktop Twitter only).
Replace bananas with pears and press ‘go’.