To comprehensively utilize construction waste bricks and industrial byproducts, a geopolymer recycled brick aggregate concrete-filled circular steel tube (GRBCFT) column is proposed. Four GRBCFT column specimens were subjected to cyclic lateral loading tests, varying brick aggregate replacement ratios and steel tube thicknesses as experimental parameters. These tests were followed by a parametric analysis using the finite element method. The results indicate that (1) GRBCFT columns failed in a compression-flexure mode, characterized by steel tube buckling at the base and crushing of the geopolymer recycled brick aggregate concrete; (2) specimens exhibited favorable deformation capacity, with ultimate drift ratios ranging between 4.5% and 6.1%; (3) the brick aggregate replacement ratio had limited impact on the lateral bearing capacity, with an increase from 30% to 70% causing only a 5.3% reduction in peak lateral bearing capacity; and (4) lateral bearing capacity and ductility decreased rapidly when the axial compression ratio exceeded 0.4. A restoring force model describing the relationship between lateral load and drift ratio was developed based on experimental and numerical results, accurately predicting the hysteretic behavior of GRBCFT columns under lateral loading.