State Witness Protection Act of 2013 - Amends the federal criminal code to impose criminal penalties on any person who kills, or attempts to kill, a witness in a state or local judicial proceeding, who uses physical force or the threat of force against such a witness, or who offers such witness anything of value with the intent to: (1) influence, delay, or prevent the testimony or attendance of such witness at a state or local judicial proceeding; (2) prevent the production of a record or document in a state or local judicial proceeding; (3) cause or induce any person to withhold testimony or evidence, destroy evidence, evade legal process, or be absent from a state or local judicial proceeding; (4) hinder, delay, or prevent any person from providing information to a state or local law enforcement officer or judge; or (5) retaliate against any person for attending a state or local judicial proceeding or providing information to a law enforcement officer.

Directs the U.S. Sentencing Commission to amend guidelines to increase the sentencing range for obstruction of justice if such crime involved threatening, harming, or bribing a witness or the destruction of evidence.

Directs the Attorney General to make competitive grants to eligible state, tribal, and local governments to establish or maintain programs that provide: (1) protection or assistance to witnesses in court proceedings involving homicide, a serious violent felony or drug offense, gangs, or organized crime; and (2) information and outreach to the public about witness intimidation. Sets forth criteria by which the Attorney General shall evaluate applicants, including the extent to which: (1) an applicant has a lack of infrastructure to support a witness assistance program, and (2) witness intimidation is present with respect to the applicant.