The most common and most likely answer to this crossword clue is the 4 letter word GAGS
I've seen this crossword clue in The Guardian
G
A
G
S
More clues leading to the result GAGS
Buddy explains!

The straight part
We know that "Makes sick/jokes" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case makes sick/jokes = gags.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does GAGS mean?
GAGS noun- A device to restrain speech, such as a rag in the mouth secured with tape or a rubber ball threaded onto a cord or strap.
- An order or rule forbidding discussion of a case or subject.
- A joke or other mischievous prank.
- A device or trick used to create a practical effect; a gimmick
- A convulsion of the upper digestive tract.
- A mouthful that makes one retch or choke.
- Mycteroperca microlepis, a species of grouper.
- To experience the vomiting reflex.
- To cause to heave with nausea.
- To restrain someone's speech by blocking his or her mouth.
- To pry or hold open by means of a gag.
- To restrain someone's speech without using physical means.
- To choke; to retch.
- To deceive (someone); to con.