Your question seems to presuppose that one chooses whether to be convinced by an argument or whether to believe that one has free will. I don't find that presupposition to be psychologically plausible, and indeed it might be conceptually incoherent. Besides, wouldn't you rather form your belief because of a compelling argument than because of something else? You'll find relevant discussion in this online article.
In any case, determinists -- who say that all events, including all human choices, are causally determined by prior conditions -- can grant that one chooses whether to be convinced by an argument or whether to believe that one has free will. According to determinism, such a choice will be causally determined by prior conditions, including any arguments to which the chooser has been exposed. It could be that the logical virtues of some argument are among the conditions that cause someone to choose to accept its conclusion. So I see nothing paradoxical about a (hard or soft) determinist's trying to cause someone to (choose to) believe a particular proposition by presenting that person with an argument for it. Even if the person currently rejects the proposition, and was causally determined to reject it, exposure to an argument can change his or her mind about it. Determinism doesn't say that what you believe has nothing to do with the arguments you encounter: on the contrary, determinism says that the arguments you encounter can matter crucially to what you end up believing.