Offending Oil Polluters Act of 2013 - Amends the Internal Revenue Code to deny all income tax credits and deductions to an offending oil polluter. Defines "offending oil polluter" to mean any person responsible for a vessel or a facility from which oil is discharged, unless such person: (1) has met all obligations under the Oil Pollution Act of 1990 to provide compensation for covered removal costs and damages; (2) was not found during the seven-year period after the first oil discharge to have committed willful or repeated violations under the Occupational Safety and Health Act of 1970; (3) was not convicted of a criminal violation for death or serious bodily injury; (4) did not have more than 10 fatalities at its facilities or refineries resulting from violations of federal or state health, safety, or environmental laws; and (5) was not required to pay fines of more than $10 million for violations of the Federal Water Pollution Control Act (commonly known as the Clean Water Act) or the Clean Air Act.