Yes. Tax withheld counts as paid evenly through the year no matter when it comes out, so one December RMD with enough withholding covers all four quarters.
An estimated payment counts on the day the IRS receives it. Withholding is different. Form 2210 treats every dollar withheld during the year as paid in four equal installments on the four due dates, and tax your IRA custodian withholds from a distribution is withholding. So a required minimum distribution taken in December with a large withholding election is credited to April, June, and September as if you had paid on time.
The amount to withhold is your safe harbor number, 100% of last year's total tax or 110% if your adjusted gross income was over $150,000, minus whatever is already being withheld from Social Security or a pension. If this year's tax will be lower than that, the current-year figure works too. Custodians withhold a default 10% from an IRA distribution unless you elect a different rate on Form W-4R, and you can pick any whole percentage up to 100. The RMD tax calculator turns the dollar amount into that percentage.
The catch is that withholding can only come out of the distribution itself. A $30,000 RMD can send the IRS at most $30,000, and what it sends does not reach your bank account. If your safe harbor number is larger than the RMD, take a bigger withdrawal or cover the difference with a quarterly payment. Custodians also set a cutoff, often mid December, for distributions that count in the current year, so do not leave it for the last week.
Nothing special goes on the return. Form 1099-R reports the withholding in box 4, it flows to the withholding line of Form 1040, and the IRS applies the even-installment treatment on its own. Form 2210 has a box to use actual withholding dates instead, which you would only check when withholding was front-loaded, never for a December RMD.
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Sources: Form 2210 instructions· About Form W-4R· IRS Publication 505