The question is not whether or not you may use expletives in academic writing, but whether or not that quote is essential for your argument.
Academic writing must not be filled with what that older fellow in your life would have called "shit". Academic writing must be clear, concise and to the point. Don't meander.
But this also means that if you need to express a certain thought, or if illustrating your argument with an example will make it easier to understand, you should not talk around this but say it directly. You are among adults and you don't need to censor your language for the sake of propriety.
For example, in an essay on expletives, it would be completely inappropriate not to give examples. Expletives are a valid field of research and many academic publications not only study but quote them extensively.
On the other hand you must be aware how pushing at the limits of propriety can make you feel edgy and cool and reflect whether you don't actually want to use that quote for its shock value.
Certainly vulgar terms should not be part of your own writing, but if they are part of a source you cite, there is nothing you need to worry about. If – and that is what you need to worry about with each source you cite – that source is citable1 and the citation furthers your argument.
If you feel that the meaning of the citation is necessary but that its wording is problematic, you can paraphrase that sentence. You might even want to try that just to see if the citation is actually necessary: if a paraphrased version no longer feels informative, then probably the citation itself is only interesting to you because it contains that one vulgar word, and you should drop it.
It would strongly advise against replacing words in a citation.
1 A word on citability: I do not know what kind of essay you write, and the APA style is applied to all kinds of writing that is not academic in the strictest sense, but nevertheless you must consider the following criteria before you include a citation in your writing (from Wikipedia):
- Credentials / Authority — Is the author(s) qualified? Why can we beleive this source?
- Accuracy — How accurate is the information? Can the information be verified in other respected sources?
- Currency — Is the information’s publishing date current enough for the topic of the research paper?
- Point of View / Objectivity — Does the author or publisher express an opinion? Does bias affect the information’s accuracy?
- Relevance — Does the information help answer your research question?
- Who is the information written for? Is the audience focus appropriate for a research paper?
In academic writing, only peer reviewed sources are citable. You probably don't have to go that far, but taking a minute to understand how the peer review process works and what purpose it serves will give you an insight that will help you more critically consider your own sources. And if you don't have time to do this before you have to hand in this essay, make sure you educate yourself in time for your next assignment.
Good luck, and let us know what your professor answered.