But now I started to think this could be true to certain extent. There were collections of such jokes printed abroad and smuggled into USSR. This does not mean they were printed by CIA, of course. But there is also tone of those jokes.
They were not the kind of jokes that point out something like low quality of goods or services (Reagan retold a few of these; such jokes were widespread and absolutely legal, there were numerous official satirical magazines that had them in spades). These was, for example, a series of jokes about a certain Civil war figure. There was a movie about him ("Chapaev", last name) that was immensely popular in USSR. In the series of jokes he and his comrades appeared as the filthiest and stupidiest scoundrels. There also was a serie of jokes about "War and Peace" figures (Rostova, Bolkonsky, etc.), with exactly same approach.
What started that process was a rather dull and artificial joke that turned out to mock an end scene of some war movie. I somehow missed that movie in my youth, but I knew the title of it, the movie and the book it was based on were well known. But once I saw it I clearly saw that the joke was meant to mock the movie; there is no other explanation.
Thing is, the scene should not be mocked. William James wrote that a characteristic quality of a religious experience was a feeling of seriousness; "not all is vanity". This feeling was very alive in USSR, even though it was a formally atheist country. We clearly understood that as kids. Not because you will be punished, mind you, but because this will harm you.
With that understanding I reevaluated the other jokes and indeed the intent was same. I also remembered certain songs that also appeared about that time; they were called "emigrant songs" and, apparently, they were recorded in Russian neigbourhoods of New York. They were in fantastically bad taste; yet they were everywhere.
Bad taste and bad jokes don't need CIA; but now I think CIA indeed played a part by giving all that a much bugger scale that might have happened organically.