Havard’s Dataverse project has, among other things, a downloadable dataset of “all known publicy available tweets for Donald J. Trump’s (@realdonaldtrump) Twitter account” as a JSON file.
This data was compiled from multiple sources including several online Github accounts that contained the status ids for previous tweets made by Donald Trump. All ids were compiled into a single list and then those ids were requested from Twitter’s “statuses lookup” endpoint. Tweets deleted by Donald Trump will not be in this dataset but can be obtained from the author of this publication for a subset of the time range present in this dataset. This dataset will also include the tweet information for any retweeted tweets under the “retweeted_status” key for each JSON object. The user object has been left in each tweet (both the main tweet and retweeted / quoted tweets if they exist).