Skills Investment Act of 2013 - Amends the Workforce Investment Act of 1998 (WIA) to direct the Secretary of Labor to make grants to states to establish programs for federally tax-exempt portable lifelong learning accounts containing cash contributions made by an eligible worker, the worker's employer, or a third party, or which may be made by the worker and matched by the employer, in order to pay certain education and skill development expenses to bolster the worker's existing career or transition to a new career.

Requires each account to be established as a trust administered by a governor-designated entity meeting certain requirements.

Defines "eligible worker" to mean an individual who: (1) is age 16 or older; (2) has a federally-tax exempt lifelong learning account; and (3) is employed, self-employed, or had been previously employed and is looking for work.

Requires a state governor to submit for Secretary approval a five-year state supplemental plan meeting specified minimum requirements.

Requires states to use grants to: (1) establish lifelong learning accounts programs; and (2) assist one-stop centers to provide career information, guidance, and related activities for workers seeking to establish or use a lifelong learning account, as well as information on education and skill development programs or courses of eligible providers. Authorizes a state also to use a portion of grant funds to make contributions to lifelong learning accounts meeting state criteria, such as accounts to which small- and mid-sized employers have made contributions or accounts of lower-income eligible workers.

Prescribes other state level activities and the responsibilities of state boards.

Requires local boards to submit for state governor approval local supplemental plans consistent with state supplemental plans.

Requires a trustee to establish and manage lifelong learning accounts in accordance with certain requirements.

Sets at 80% the federal share of costs for administering a lifelong learning accounts program.

Requires the Secretary to study whether, and to what degree, states should be permitted to use grant funds to make contributions to the lifelong learning accounts of eligible workers in the state.

Amends the Internal Revenue Code to: (1) allow employees a tax credit for contributions made to a lifelong learning account; (2) exclude from employee gross income any employer contributions to a lifelong learning account; (3) exempt lifelong learning accounts from federal income, Social Security, and railroad retirement taxation; (4) include any distributions out of the lifelong learning account in an account beneficiary's gross income; and (4) allow small employers a special tax credit for contributions to lifelong learning accounts of their employees and for associated administrative costs.