We report, to the best of our knowledge, the first demonstration of integrated electro-optic (EO) phase shifters based on racetrack microresonators on a 3C silicon-carbide-on-insulator (SiCOI) platform working at near-infrared wavelengths. By applying DC voltage in the crystalline axis perpendicular to the waveguide plane, we have observed optical phase shifts from the racetrack microresonators whose loaded quality ($ Q $) factors are $\sim\! {30,\!000}$. We show voltage-length product (${{V}_{\pi}} \cdot {{L}_{ \pi}}$) of ${118}\;{{\rm V}\cdot{\rm cm}}$, which corresponds to an EO coefficient ${{r}_{41}}$ of 2.6 pm/V. The SiCOI platform can be used to realize tunable silicon carbide integrated photonic devices that are desirable for applications in nonlinear and quantum photonics over a wide bandwidth that covers visible and infrared wavelengths.