Yes the phone calls made by and made to the President of the United States are recorded in the interest of national security but the leaking of those recordings are breaches of national security unless explicitly authorized. Only people with a Yankee White security clearance will normally have access to these recordings and since they are expected to have undying loyalty to the United States it is unlikely to happen.
Source :
Donald Trump's Tweets.An example may be found here
Sometimes phone calls may be recorded by someone under their direction for record keeping or future use.
Another source (IEEE) - Link
The Presidential Records Act article may prove useful.
https://twitter.com/realDonaldTrump/status/863007411132649473?ref_src=twsrc%5Etfw&ref_url=http%3A%2F%2Fwww.politifact.com%2Ftruth-o-meter%2Farticle%2F2017%2Fmay%2F12%2Fcan-presidents-secretly-record-white-house-conver%2F&tfw_site=politifact
https://www.politico.com/interactives/databases/trump-white-house-visitor-logs-and-records/index.html
TRUMP MENTIONED COMEY AS WELL THIS STREAM