In this contribution, we demonstrate the first integrated gallium arsenide (GaAs) ring resonator for second harmonic generation (SHG) on a GaAs-on-insulator platform. Such resonators exhibit high nonlinear optical coefficients, a strong optical confinement, and intrinsic quality factors exceeding 2.6 Å~ 105, which makes them very attractive for nonlinear optical applications. The fabricated resonators exhibit a great potential for frequency conversion: when 61 μW of pump power at 2 μm wavelength is coupled into the cavity, the absolute internal conversion efficiency is 4%. We predict an external SHG efficiency beyond 1 000 000%/W based on the GaAs resonance devices. Such nonlinear resonant devices of GaAs and its aluminum GaAs alloy can be directly integrated with active components in nonlinear photonic integrated circuits (PICs). This work paves a way for ultra-high efficient and compact frequency conversion elements in PICs.