Medicare Link Act of 2013 - Amends title XVIII (Medicare) of the Social Security Act (SSA) to direct the Secretary of Health and Human Services (HHS) to establish a Medicare Link Program through which individuals entitled to enroll in a Medicare Advantage (MA) plan under Medicare part C (Medicare+Choice), but who are not enrolled in one, are eligible to enroll with a nongovernmental Medicare Link contractor which shall provide: (1) a specified variety of optional care management services as well as coverage of the same items and services covered under Medicare parts A and B, and (2) a reduction or rebate in the premium otherwise applicable under Medicare part B as well as in cost-sharing.