Trump is known for his prominent use of the social media site, and has been criticised for the way he has used his account in the past - with controversial comments and unfounded statements and claims a regular occurrence during the presidential campaign.
"The Twitter Rules prohibit violent threats, harassment, hateful conduct, and multiple account abuse, and we will take action on accounts violating those policies," a spokesman said.
The site added that if explicit threats were made from Trump's account Twitter would ban him from using the service. A move that would likely damage the president-elect, as social media has been one of his most powerful tools when looking to spread his message.
Twitter has stepped in and banned users before, most notably alt-right commentator Milo Yiannopoulos, who was permanently booted from the site earlier this year after his abuse of Ghostbusters star Leslie Jones.
Trump's Twitter account features a mixture of posts from both the businessman and his team, with many of those seemingly coming from Trump appearing at strange hours of the day and often attacking his critics.