The Rydberg constant is a fundamental physical constant related to the hydrogen atom's energy levels. The Rydberg constant has units of \( \text{cm}^{-1} \), and it is used to describe the wavelengths of spectral lines of hydrogen.
Thus, the constant that has units of \( \text{cm}^{-1} \) is the Rydberg constant.
Thus, the correct answer is: \( \boxed{\text{Rydberg constant}} \).