Unfortunately, no. If you have a loss on the surrender of a non-qualified annuity, there is no tax deduction for it, but there would be no income tax on the distribution either; the information TurboTax would need to calculate this would be included on the 1099-R. For example look here: http://www.irs.gov/pub/irs-prior/f1099r--2016.pdf
Non-qualified annuities give a nice tax benefit in that tax is deferred inside them as value grows above cost basis, but when distributed, the gain is taxed first at ordinary income tax rates, not capital gains. You may not take a capital loss as you do with a stock sale.
If you have additional questions or details regarding this, please feel free to post in the comments for further clarification.
