Yes. If you open a Traditional IRA and make contributions by April 18, 2017 and designate that these contributions are for 2016, at the time that you make the contributions, you can take a deduction for these contributions if you meet the requirements to deduct them.
Generally, you can deduct the total amount of your contributions unless you or your spouse have an employer sponsored retirement plan. You can file your tax return prior to making these contributions as long you actually make the contributions by April 18, 2017.
Whether or not you can take a deduction for your Traditional IRA contributions, depends on whether or not you or your spouse (if married filing jointly) are covered by an employer sponsored retirement plan. If one or both of you are covered by an employer sponsored retirement plan, then your deduction might be reduced or eliminated based on your modified adjusted gross income and your filing status.
To determine your modified adjusted gross income, please see Worksheet 1-1 on page 15 of Pub 590A. https://www.irs.gov/pub/irs-pdf/p590a.pdf
Please refer to Table 1-2 and Table 1-3 on page 13 of Pub 590A to see if your deduction will be limited. If you are collecting social security, do not refer to these tables. Instead, see page 12 of Pub 590A under "social security recipients" for more information.
If your deduction will be limited, then you can use Worksheet 1-2 "figuring your reduced IRA deduction" on page 17 of Pub 590A, to determine the amount of your deduction.