Trump can’t cancel the Iran deal, because the Iran deal is not a bilateral agreement. It is a multilateral agreement, which means that it’s not just between the US and Iran. It’s a deal struck by the US, Iran, three European States, Russia and China.
That said, if Trump had a mind to, he could cancel America’s participation in the deal. He could ask Congress – and Congress being very hawkish on Iran would no doubt acquiesce – for a restoration of the American sanctions that existed prior to 2015. But the difficulty of doing so would be that they would not be accompanied by European sanctions or Russian sanctions. And the Europeans and Russians, having not seen any evidence that the Iranians have been cheating on the deal, would have no incentive to go back in with the US. They also wouldn’t want to undercut their own businesses who are currently exploring opportunities in Iran. So it would leave the US in a much weaker position to gain economic leverage over the Iranians.
"Although I think Donald Trump will make a lot of noise about the deal, at least in the near term I don’t really see him cancelling it."
The other thing to bear in mind is that Iran has to balance two opposing interested parties in two different conflicts. In Syria, Iran is engaged alongside Russia. It’s played a significant role in the battle to retake Aleppo from the rebels. But Iran also engaged alongside the US in Iraq. To alter the nuclear deal would mean upsetting the alliances in Iraq that the US already enjoys. So Iran has a lot of strategic leverage.
Although I think Donald Trump will make a lot of noise about the deal, at least in the near term I don’t really see him cancelling it. There are a lot of very good reasons not to. And people who have been close to Trump and who were critics of the deal when it was being negotiated have said plenty of things to back this assertion up, including James Mattis who’ll be his secretary of defence. In a way, Donald Trump was the only Republican in the running who might not have cancelled the deal immediately on ideological grounds. That’s because his criticism of the deal was based on his conviction that it didn’t give enough opportunities for American businesses which want to trade with Iran. He didn't have the same kind of ideological criticism of doing business with an avowed enemy of the United States that someone like Ted Cruz or Marco Rubio had.
Much to Trump’s chagrin; he cannot cancel the Iran deal. It’s multi-lateral, as 3 European Nations, Russia and China are involved in this as well. If he attempts to back off from this agreement, there will be international repercussions that will reverberate throughout this century