Maybe. But, probably not. It's complicated.
First, it will only be deductible if you itemize deductions. State income tax paid, in 2023, is deductible on your 2023 federal return (as an itemized deduction) regardless of which year the state tax was for.
However, if you do itemize deductions, you most likely already deducted that on your 2022 tax return. Most people take their state tax deduction based on what was withheld (and/or estimated quarterly payments) during 2022, not their final calculated tax.