Donating an annuity with a cash surrender value higher than your investment will trigger taxable income in the year of transfer. Taxable amount will be the difference between the cash surrender value and your investment.
The value of the annuity can still be deducted as a charitable contribution if you itemize deductions.
If you donate the annuity before you turn 59 ½ you will owe a 10% penalty on the early distribution.
If you are trading one annuity for another it must be done as a direct exchange to avoid income tax.