Then he sent another in which he posed next to a woman with a cigar in his mouth.
As of 11:30 A.M. ET, Bess hadn't deleted any of the tweets, but screen grabs have been posted below.
According to the Cleveland Plain Dealer, this isn't the first time Bess has shared those types of photos on social media. In December, he posted a picture on his now-shuttered Instagram account showing him sparking a cigar or cigarillo.
A spokesman for the Browns said the team "is aware of the photos and looking further into the situation and will deal with the matter internally."
Pot is among the National Football League's banned substances, but league commissioner Roger Goodell signaled this week that he's open to the idea of allowing medical marijuana to be used by players.