Improving Security for Investors and Providing Closure Act of 2013 or Improving SIPC Act of 2013 - Amends the Securities Investor Protection Act of 1970 with respect to any action in a U.S. district court by the Securities and Exchange Commission (SEC) against the Securities Investor Protection Corporation (SIPC) in the event that SIPC refuses to commit funds or otherwise act for the protection of customers of any SIPC member (debtor broker or dealer).

Authorizes SIPC, at the time the SEC action initiates such action, to allow all customers of the debtor broker or dealer to elect to receive a one-time payment from the SIPC Fund.

Prescribes procedures for such customer election. Limits the amount paid to a customer under such election to the lesser of: (1) the customer's net equity claim against the debtor, and (2) a $500,000 cap on one-time payments.

Subrogates SIPC to all rights of the customer receiving a one-time payment against the debtor once the customer recovers an amount equal to the customer's net equity claim against the debtor.

Treats a certificate of deposit (CD) purchased by a person through an account with the debtor as cash deposited and held by the debtor in an amount equal to the amount the person paid for the CD, less any amounts paid to such person on the CD.

Permits a person prevented from making an election under this Act because SIPC does not identify such person as a customer of the debtor to challenge that determination in federal district court.