Victory in an electoral college system is something Trump understands. Trump said turning to Perry before the call according to a video posted by RTE.
Mr. Varadkar raised the case of the undocumented Irish in the USA and there was a discussion on climate change and trade.
The President asked for an update on the Northern Ireland peace process and the situation regarding border controls between the North and the Republic.
Since his confirmation as Taoiseach he has spoken to the French President Emmanuel Macron, British Prime Minister Theresa May, the German Chancellor Angela Merkel and the Indian Prime Minister Narendra Modi. During the call, reporters from the Irish media were present.
Donald Trump congratulated Mr Varadkar on his appointment, and has invited him to attend the annual St Patrick's Day events in Washington next March.
Varadkar, 38, is Ireland's youngest prime minister.
"I will not, of course, rescind that invitation", he said, adding that to do so would be "inappropriate" and would create a "diplomatic incident".
Mr. Varadkar said that he will raise issues such as climate change, LGBT rights, and immigrant rights on a future USA visit.
The call lasted just under 15 minutes with topics ranging from climate change to Brexit.