American Unemployed Worker Investment Act of 2013 - Amends the Internal Revenue Code to allow a small business employer (i.e., an employer that employs more than 10 but fewer than 25 full-time employees throughout the taxable year) a work opportunity tax credit for hiring a qualified unemployment compensation recipient. Allows the first $10,000 of wages paid to such a recipient to be taken in account for purposes of such credit.

Defines "qualified unemployment compensation recipient" as any individual who is certified as: (1) not being a student for at least six months during the one-year period ending on the hiring date, (2) being in receipt of unemployment compensation on the hiring date, and (3) having a hiring date during the two-year period which begins on the enactment of this Act.

Denies such credit unless: (1) the qualified unemployment compensation recipient is employed for not less than 35 hours per week for not less than 1 year, and (2) the number of full-time employees of the employer receiving such credit is increased by 1 for at least 1 year.