Yes, a contribution made between January 1 and April 15 may apply to the prior tax year. After your tax filing due date however, you can only make a current-year contribution.
IRS Circular 230 Notice: The information contained in this FAQ is provided for information purposes only, is not intended to constitute tax advice which may be relied upon to avoid penalties under any federal, state, local or other tax statutes or regulations and does not resolve any tax issues in your favor. Refer to IRS Publication 590, Individual Retirement Accounts for additional information on IRAs in general and consult your tax advisor about your individual tax situation.