If the tweet was recently deleted and the account is public then search on Google and look in the cached version of their profile (click the small green arrow next to the address in the search results). I'm afraid this is rather pot luck. The tweet may have been sent too recently to have been indexed by Google, or too distantly in the past and Google's later indexing will have overwritten it. But I have found several deleted tweets in this way, which allows a subsequent screenshot to be taken. Bing also indexes tweets so worth searching there too.

A tweet, while it was still 'live'. may have been captured in Storify or other tools so it may be worth having a look there too - here's an example of one of my own tweets that I storified years ago then deleted and it's still there! What happens when a tweet used in Storify is deleted?

If it was a controversial tweet then search for tweets sent in reply to the person who sent it, or for words that were in the tweet. The chances are that someone else will have saved a copy or manually retweeted it (making the text searchable) or taken a screenshot and mentioned it to them.

If you want to pre-emptively capture the tweets of someone who has a tendency to delete them later then you could use something like IFTTT to send you an email each time they tweet. Your copy will remain even if they subsequently delete the original. source: https://www.quora.com/How-can-I-find-a-Tweet-that-someone-has-deleted