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It doesn’t take a holiday for Senator Rand Paul to dish some snark to his opponents on social media, but in the spirit of “Festivus,” the Republican from Kentucky has stepped up his game.

In what has become an annual tradition, Mr. Paul spent Wednesday sending Twitter messages with some of his most heartfelt grievances, including a few for his fellow presidential hopefuls.

Mr. Paul’s gambit embraces the fictional holiday — “Festivus … for the rest of us!” — which was created by Frank Costanza from “Seinfeld” and caught on in popular culture. One of the rituals performed by those who celebrate is an “airing of grievances,” during which family members share their biggest disappointments with one another over dinner.

Mr. Paul managed to get in a dig at Hillary Clinton’s restroom delays, noting that Carly Fiorina has had no issues making it back onto the debate stage by the time the commercial break concludes. He took at dig at Donald J. Trump’s made-in-China line of neckties and the billionaire developer’s grasp of Yiddish.

Spreading cheer across the crowded field, Mr. Paul also poked Gov. Chris Christie for his Dallas Cowboys fandom and Senator Marco Rubio for failing to show up for work.

to my absentee friend @marcorubio, I didn't put your $170k+ salary in my waste report today. But I could have #Festivus — Dr. Rand Paul (@RandPaul) December 23, 2015

Senator Lindsey Graham was let off the hook because he dropped out of the race this week, but Ben Carson’s soft-spoken style proved to be an easy target for Mr. Paul.

I have no grievances against my fellow doc @RealBenCarson because I have not heard a word he has said in any debate. #Festivus — Dr. Rand Paul (@RandPaul) December 23, 2015

Mr. Paul’s humor was not appreciated by supporters of some of his opponents, who suggested that the jokes were cheap shots. A few advised the low-polling senator to focus on his struggling presidential campaign or to save his zingers for the debate stage — if he qualifies for the next one.