Rectangular graphene loop antenna for terahertz (THz) band is proposed and analyzed. Symmetry properties of the antenna in terms of currents and the radiated fields are investigated. By means of numerical simulations, the antenna is analyzed in free space and on a semi-infinite substrate. It is shown that the maximum total efficiency and minimum input reflection coefficient occur around the second resonance frequency of the antenna. Depending on the relative permittivity of the semi-infinite substrate considered in this article (from 1 to 3.8), the maximum total efficiency of the proposed antenna ranges from 50.1% to 57.4% and its fractional bandwidth (BW) is between 85.2% and 96.6%. Fractional BW of loop antenna can be approximately twice that of graphene dipole antenna and maximum total efficiency can be about 14% higher. BW augmentation is explained using developed equivalent circuit models for dipole and loop antennas. It is also shown that under specific conditions, the radiation pattern of the proposed device can be approximated by an equivalent scheme of two coupled small electric dipole antennas. Finally, we demonstrate that the proposed antenna tolerates moderate variations of graphene parameters.