Donald Trump's Twitter engagement is stronger than ever

Many Americans may be losing patience with President Donald Trump's Twitter account, but that hasn't kept his tweets from getting millions of favorites and retweets since his inauguration.

Americans from both parties have told pollsters that Trump should shut down his personal Twitter feed, but engagement with the account has skyrocketed since the Jan. 20 inauguration.

In the month since the ceremony, favorites have been about twice what they were after the election, when Trump's tweets criticizing companies and selecting Cabinet members made national news. Thirty-three of the top 50 most-favorited Trump tweets were from this year, and retweets showed a similar pattern.

President Barack Obama activated the first presidential Twitter account in May 2015, gaining hundreds of thousands of followers for the @POTUS account in a matter of minutes. The Trump administration inherited that account in January, along with its 14 million followers.

Obama handed over his named social media accounts, including @BarackObama, his account during the campaign, to an independent nonprofit group in January 2013. But Trump opted to keep his personal account — and its millions of followers — as a primary communication channel.

"I'd rather just let that build up and just keep it @realDonaldTrump," Trump told the Times of London in January. "It's working."

Although some reports indicated that Trump would not use the @POTUS account, he has been making use of both accounts, signing some @POTUS tweets "-DJT." So far, it appears that the @POTUS account is putting out staid administrative tweets, while the @realDonald Trump contains more of the off-the-cuff attacks that won the campaign so much attention during the election.

Before the election, Trump's account had about 13 million followers. By Jan. 20, the account had hit 21 million, and today it has about 25 million. Favorites and retweets have increased even more than the number of followers, according to data pulled by CNBC from the Twitter API.

Trump's use of Twitter can have real consequences for companies like Boeing, General Motors, and Ford, which have found themselves in the president's crosshairs on the social media platform. According to a recent analysis, Trump's negative tweets targeting companies encouraged other users to attack those companies as well.

But at least one company is enthusiastic about the president's relentless tweeting: Twitter itself. While he noted that a single person can't drive sustained growth, Twitter CEO Jack Dorsey said on the company's earnings call last week Trump has helped the platform at the "macro level."

"The President's use of Twitter has broadened the awareness of how the platform can be used, and it shows the power of Twitter," said Dorsey. "When he tweets, it sparks conversation and discussion."

Dorsey bought $7 million worth of shares in the company this week, according to regulatory forms filed on Tuesday.

Despite the popularity of Trump's personal Twitter account, it's still about 60 million followers behind @BarackObama. The former president tweeted that he was retaking control of his old handle on Jan. 20, a tweet that received 1.9 million favorites and almost 450,000 retweets. None of Trump's recent tweets has come close to those figures.