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The first day to file taxes with the IRS will officially start on January 23. However, you can get started at anytime with online tax filing and get your refund as soon as possible. Four out of five returns have also been projected to be prepared using tax return software and e-filed.
If you mean personal income taxes, you can file them any time after January 1, and they are due on or before April 15, unless you file for an extension. In USA, you may file personal income taxes beginning January 2 and the deadline is April 15 or the first business day thereafter.