I know of no research showing a correlation between IQ and the use of profanity. However, I would conjecture that there is a modest correlation between those two variables. Why?
People usually resort to profanities when they are frustrated and are having trouble coping. This is much more likely to happen among those of low IQ for whom life offers what appear to be insurmountable challenges. Imagine how difficult it must be to navigate through computer technologies or complicated procedures for those with learning difficulties. Every new learning experience becomes a challenge and when the challenge is overwhelming, the only possible response is frustration and anger. A person of high IQ when confronted with an intellectual challenge usually slips into problem solving mode with the confidence that a solution will appear. Anger is an emotion that is probably more prevalent in those of moderate to low IQ.
Profanity is also the default mode of expression when the appropriate vocabulary is not available. This is more likely to occur among those of limited vocabulary skills and low IQ. Those of higher IQ are usually equipped with a much larger vocabulary to express themselves and they resort to profanity only in situations of extreme emotion when a more sanguine response is inaccessible.
A third factor that contributes to a correlation between the use of profanity and IQ is social background. Those who come from sophisticated backgrounds where ideas are discussed at a cerebral, rather than a visceral, level are accustomed to discussing ideas without excessive emotion or the use of profanity. By contrast, those who come from unsophisticated backgrounds seldom engage in cerebral conversation. Communication is usually visceral, dealing with emotional exchanges involving forceful argument, coercion, or intimidation. Many profane words are aggressive and serve the purpose of intimidation better than milder forms of expression. Compare the assertion, “I wish you would depart,” with the expression “F**k off.” People of high and low IQ will both use the latter expression on occasion, but the lower IQ folks will probably use it more often.
These comments are based only on my experiences and conjectures, and are not supported by any research of which I am aware. If you are frustrated by the lack of research backing this answer, and you have high IQ, you might respond, “Oh frig!”