Cyclic response of "shear" connections between steel outrigger beams and reinforced concrete core walls is presented in this paper. The connections investigated in this paper consisted of a shear tab welded onto a plate that was connected to the core walls through multiple headed studs. The experimental data from six specimens point to a capacity larger than the design value. However, the mode of failure was through pullout of the embedded plate, or fracture of the weld between the studs and plate. Such brittle modes of failure need to be avoided through proper design. A capacity design method based on dissipating the input energy through yielding and fracture of the shear tab was developed. This approach requires a good understanding of the expected capacity of headed studs under combined gravity shear and cyclic axial load (tension and compression). A model was developed and verified against test results from six specimens. A specimen designed based on the proposed design methodology performed very well, and the connection did not fail until shear tab fractured after extensive yielding. The proposed design method is recommended for design of outrigger beam-wall connections.