Restoration of Parental Rights and State Sovereignty Act of 2013 - Amends the Elementary and Secondary Education Act of 1965 (ESEA) to prohibit the Secretary of Education from forcing a state to satisfy any requirement imposed as a condition of receiving assistance under an ESEA grant program.

Prohibits the Secretary from releasing assistance to a state under an ESEA grant program unless the state's legislature has by law expressly approved the program. Allows that approval to be accomplished by a vote to affirm a state budget that includes the use of such federal funds, but requires that budget to expressly include any requirement imposed as a condition on the state's receipt of those funds.

Prohibits ESEA funds that are not allocated to a state due to the state's failure to affirmatively agree to their receipt from being reallocated among the other states.

Expresses the intent of Congress that control over public education and parental rights to control their children's education is vested exclusively within the authority reserved to the states and individual Americans by the Constitution, except when states expressly approve federal terms or conditions on educational assistance or the federal government is obliged to enforce minimum federal equal protection or due process standards.