This strategy was much more effective if you purchased the annuity on or before December 20th, 2002. The strategy is not as common now as the tax rules have changed, but you could still purchase an annuity from a charity now and receive some tax savings. A donation would be eligible for the tax credit if the amount you pay the charity for the annuity is more than what you would normally have paid for it from a financial institution offering annuities.
For example, if you had gone to a life insurance company and asked for a quote for an annuity they might tell you that every $100,000 given to them will give you $1,000/month for the rest of your life (this is based on their actuarial estimation of your life expectancy, prevailing interest rates and interest rate forecasts, an added cushion for profit, etc).
To be eligible to receive any type of tax credit for a donation, you would have to pay more than $100,000 to a registered charity for that same $1,000 monthly payment. If you just paid the market rate, then you wouldn’t really have made a charitable contribution to them as they did not benefit from the transaction in any charitable way.
Before the rules changed, the monthly payments could have been tax-free to you – now, a portion of the payments may be taxable: more reason why this strategy is not very common. If you are interested in such a strategy, it is highly recommended that you speak with a tax specialist to go over all the intricacies.