Industrial robots are more compliant than CNC machine tools, which makes them prone to chatter during robotic milling. Chatter has slowed down the adoption or sometimes inhibited the use of robots for machining tasks. This work presents a new chatter suppression scheme by mounting a magnetorheological fluid (MRF) absorber on the spindle housing to absorb the vibration with a specific frequency range. Firstly, a Gaussian process regression (GPR) model is used to predict the modal parameters at different machining positions. Subsequently, the predicted modal parameters are employed as input to obtain the transfer matrix for chatter frequency calculation. After that, a novel MRF absorber is designed based on the controllable shear modulus of the MRF in its pre-yield region. The simulation verifies that the designed MRF absorber can suppress chatter and thus improve the surface quality of the workpiece.