Some researchers have published:
2016 United States Presidential Election Tweet Ids dataset
... the SFM team is sharing the tweet id of every single tweet that we collected around the election – all 280 million of them. The tweets are broken up into 12 collections:
Candidates and key election hashtags (Twitter filter)
Democratic candidates (Twitter user timeline)
Democratic Convention (Twitter filter)
Democratic Party (Twitter user timeline)
Election Day (Twitter filter)
First presidential debate (Twitter filter)
GOP Convention (Twitter filter)
Republican candidates (Twitter user timeline)
Republican Party (Twitter user timeline)
Second presidential debate (Twitter filter)
Third presidential debate (Twitter filter)
Vice Presidential debate (Twitter filter)
Link to data
Twitter's terms of service state that you can't share the tweet content, and only the tweet id. This is to allow users to delete the content, and keep the right to be forgotten.
When you have a list of tweet ids, you can retrieve the tweet content, assuming it hasn't been deleted.
The Twitter API endpoint to retrieve a tweet based on its id is here: https://developer.twitter.com/en/docs/tweets/post-and-engage/api-reference/get-statuses-show-id.html
or up to 100 tweet ids at a time: https://developer.twitter.com/en/docs/tweets/post-and-engage/api-reference/get-statuses-lookup
There are tons of programming libraries to access the API - pick your favorite (Python, R, etc) and search for the best.