Tax Credit for Early Educators Act of 2013 - Amends the Internal Revenue Code to: (1) allow an individual taxpayer who is employed in a position involving regular contact with students in an early childhood school or education program and whose position involves the formulation or implementation of educational programs for such school or program a $3,000 tax credit, adjusted for inflation after 2013; (2) extend until 2018 the tax deduction for certain expenses of eligible educators (currently, elementary and secondary school teachers) and expand the definition of "eligible educators" to include teachers, instructors, counselors, or aides in a preschool or early childhood program; and (3) eliminate the income-based reduction in the tax credit for employer-provided dependent care services (thus allowing a full 35% tax credit for employment-related expenses incurred for the care of a dependent).