An electric method for measuring magnetic anisotropy in antiferromagnetic insulators (AFIs) is proposed. When a metallic film with strong spin-orbit interactions, e.g., platinum (Pt), is deposited on an AFI, its resistance should be affected by the direction of the AFI N eel vector due to the spin Hall magnetoresistance (SMR). Accordingly, the direction of the AFI N eel vector, which is affected by both the external magnetic field and the magnetic anisotropy, is reflected in resistance of Pt. The magnetic field angle dependence of the resistance of Pt on AFI is calculated by consider- ing the SMR, which indicates that the antiferromagnetic anisotropy can be obtained experimentally by monitoring the Pt resistance in strong magnetic fields. Calculations are performed for realistic systems such as Pt/Cr2O3, Pt/NiO, and Pt/CoO.