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We report the real-valued static and complex-valued quasi-static anisotropic permittivity parameters of rare-earth scandate orthorhombic single crystal GdScO3 (GSO), TbScO3 (TSO), and DyScO3 (DSO). Employing continuous-wave terahertz spectroscopy (0.2–1 THz), the complex permittivity was extracted using an anisotropic ambient-film-ambient model. Data obtained from multiple samples of the same oxides and different surface cuts were analyzed simultaneously. The zero-frequency limit of the modeled data indicates that at room temperature the real part of the dielectric tensor components for GSO are ɛa = 22.7, ɛb = 19.3, and ɛc = 28.1; for DSO, ɛa = 20.3, ɛb = 17.4, and ɛc = 31.1; and for TSO, ɛa = 21.6, ɛb = 18.1, and ɛc = 30.3, with a, b, and c crystallographic axes constituting the principal directions for the permittivity tensor. These results are in excellent agreement with expectations from theoretical computations and with scarcely available data from previous experimental studies. Furthermore, our results evidence a noticeable attenuation, which increases with frequency, and are very significant especially at the higher frequency end of the measurement and along the c-direction in all samples. We suggest the attenuation is most likely caused by the onset of absorption due to long-wavelength active optical phonon modes. These results are important for electronic and potential sub-terahertz applications (e.g., quarter-wave plate) benefiting from the large index contrast along different directions in these materials.