The transfer printing of aluminum gallium arsenide (AlGaAs) microdisk resonators onto a silicon-on-insulator (SOI) waveguide platform is demonstrated. The integrated resonators exhibit loaded ${Q}$Q-factors reaching $ 4 \times {10^4} $4×104, and the vertical assembly approach allows selective coupling to different spatial mode families. The hybrid platform's nonlinearity is characterized by four-wave mixing with a measured nonlinear coefficient of $ \gamma = 325\;{({\rm Wm})^{ - 1}} $γ=325(Wm)-1, with the devices demonstrating minimal two-photon absorption and free-carrier absorption losses that are inherent to SOI at telecommunications wavelengths.