Not signifcantly. A teeny bit nagetively, but in general worth worrying about if you've otherwise got good credit. Ie, it might drop you ten or twenty points temporarily, but not cumulatively, since it'll only be affected at most by the last few months of churning at any time. (And thus if you keep churning, it'll level out, and if you decide to stop churning, the tiny negative effect will go away soon thereafter, all other things being equal.)

Your credit score is much more affected by your ratio of total credit available to total credit used, your on-time payment and always paying at least $1 more than the minimum (since they have a flag which simply say's "piad minimum" vs "paid more than minimum")*, the age of your credit history (thus cancel your most recently acquired cards, and never cancel cards you've had for decades).

And note that the latter point fits in perfectly with churning! In churning, you're cancelling the cards after you get the bonus, so you're cancelling new cards with little credit history, and thus it hurts your credit score neglibly.

Thus that only teeny negative dip on your credit score is going to be from the recent inquiry count.

And meanwhile, if you don't have much credit available at Citi now but they give you a bunch on your first card or two, then that aspect raises your credit score, so in that case it may balance out or even go net positive! But if you already have several cards with high credit available at Citi, they'll likely just shuffle that available creidt around into the new cards you apply for.

*For value reasons, of course, you always want to pay the balance in full every month. But from a credit score standpoint, all that matters is that it be at least $1 more than the minimum every month so that it's not flagged as "just the minimum", and that you keep the total balance on your cards low compared to the total credit available.