Yes, but it has been excised from all videos.
I recall seeing a brief scene (probably in the episode teaser - the opening scene before the main title) where Kirk and Spock are walking in a corridor (presumably to the transporter room), when Kirk says something to the effect of, "Crewman! Put out that cigarette!".
This was back in the 1970s and I've never seen it since. I thought it was in either "Charlie X" or "Tomorrow is Yesterday".
But, the "The Official Star Trek Trivia Book" by Rafe Needleman (1980), in question #250 asks, "In which episode do you find someone smoking on the Enterprise? To which he gives the answer, "A Piece of the Action".
I know the book has errors (for example, it states Ophiucus VI was Mudd's original destination in "Mudd's Women" - when it was Ophiucus III), which is why I am not convinced because it disagrees with my memory.
So, yes, there was a single (now excised and memory holed) scene in Star Trek The Original Series where someone was smoking a cigarette onboard the USS Enterprise.
UPDATED: 21 August-2023
In the episode "Patterns of Force", a woman is briefly seen who is holding a short (empty) cigarette holder (around 32:20):
In the episode "Spectre of the Gun", some men are seen smoking cigars (around 13:05):