I-Squared Act of 2013

Immigration Innovation Act of 2013 or the I-Squared Act of 2013 - Amends the Immigration and Nationality Act to establish an annual cap on H-1B visas (specialty occupations) at between 115,000 and 300,000 visas depending upon market conditions and existing demand. Sets forth allocation provisions.

Directs the Secretary of Homeland Security (DHS) to: (1) authorize the accompanying spouse of an H-1B alien to work in the United States, and (2) provide such spouse with an appropriate work permit.

Prohibits the Secretary of Homeland Security from denying a petition to extend the status of an H-1B or L-visa (intra-company transferee) nonimmigrant involving the same alien and petitioner unless the Secretary determines that: (1) there was a material error in the previous petition approval, (2) a substantial change in circumstances has taken place that renders the nonimmigrant ineligible for such status, or (3) new information has been discovered that adversely impacts the eligibility of the employer or the nonimmigrant.

Directs the Secretary of State to authorize a qualifying alien admitted under an E-visa (treaty traders and investors), H-visa (temporary workers), L-visa (intracompany transferees), O-visa (extraordinary ability in the sciences, education, business, athletics, or the arts or films or television), or P-visa (athletes, artists, and entertainers) to renew his or her nonimmigrant visa in the United States.

Eliminates the foreign student visa requirement that an individual has no intention of abandoning his or her foreign residence.

Eliminates the per country numerical limitation for employment-based immigrants and increases the per country family category limit. Applies such provisions beginning with FY2014.

Amends the Chinese Student Protection Act of 1992 to eliminate the provision requiring the reduction of annual Chinese (PRC) immigrant visas to offset status adjustments under such Act.

Provides for the recapture of unused employment-based immigrant visas from FY1992 through the current fiscal year.

Excludes from employment based immigrant limitations aliens: (1) who are the spouse or child of an employment-based immigrant; (2) who have a master's or higher degree in a STEM field (science, technology, engineering, and math) from a school qualified under the Higher Education Act of 1965; and (3) for whom a priority worker petition for an employment-based immigrant visa has been approved.

Increases H-1B employer fees and establishes a fee on employment-based visa petitions. Provides that such fees shall be used for STEM education and training.

Establishes in the Treasury the Promoting American Ingenuity Account to enhance U.S. economic competitiveness by: (1) strengthening STEM education and ensuring that schools have access to well-trained STEM teachers; (2) strengthening the elementary and secondary curriculum, including efforts to increase computer science course availability; and (3) helping colleges and universities produce more graduates in fields needed by American employers.

Sets forth provisions regarding: (1) fund allocations, (2) state grant applications, and (3) approved grant activities.

States that nothing in such STEM funding provisions shall be construed to permit the Secretary of Education or any other federal official to approve the content or academic achievement standards of a state.