Habeas Corpus Reform Act of 1993 - Amends the Federal judicial code to revise provisions governing habeas corpus procedures, particularly in capital cases. Establishes a statute of limitations of one year for the filing of an application for habeas corpus relief from a sentence of death. Prescribes: (1) periods during which such time requirement shall be tolled, including any period in which the State has failed to appoint counsel for State post-conviction review; and (2) conditions under which such requirement shall be tolled. Specifies requirements for stays of execution in capital cases. Bars the court from announcing or applying a new rule that changes the constitutional or statutory standards that prevailed at the time the petitioner's conviction and sentence became final on direct appeal to grant habeas corpus relief, except when such rule: (1) places a class of individual conduct beyond the power of the criminal lawmaking authority to proscribe or prohibits the imposition of a certain type of punishment for a class of persons because of their status or offense; or (2) constitutes a watershed rule of criminal procedure implicating the fundamental fairness and accuracy of the criminal proceeding. Requires that claims presented in a habeas corpus petition not timely presented in a prior petition be dismissed unless the petitioner makes a specified showing and the facts underlying the claim, if proven and viewed in light of the evidence as a whole, would be sufficient to undermine the court's confidence in the factfinder's determination of the applicant's guilt or demonstrate that no reasonable sentencing authority would have found a condition of eligibility for a sentence or would have imposed a death sentence. Sets forth provisions regarding: (1) new evidence in capital cases; (2) certificates of probable cause; and (3) assistance of counsel (requiring that every indigent capital defendant at all stages from trial through the end of the State proceedings be provided with counsel meeting specified standards of knowledge and experience in capital cases). Amends the Omnibus Crime Control and Safe Streets Act of 1968 to require the Director of the Bureau of Justice Assistance to make grants to States: (1) to support litigation pertaining to Federal habeas corpus petitions in capital cases; and (2) for State capital litigation. Authorizes appropriations. Requires States in which a death sentence may be imposed to certify compliance with counsel-related provisions or have State allocations reduced.