Orbital-selective phenomena in mutliorbital systems have received much attention due to their uniqueness as well as possible connections to other phenomena. As orbital-selectiveness is mostly related to the crystal structure, finding a new control parameter other than structure would be of significant importance. Here we report discovery of an orbital-selective doping effect in Sr2Ru1-xIrxO4 (SRIO). Our systematic electronic structure study of SRIO reveals an anomalous orbital-selective doping effect and concomitant Lifshitz transitions (LTs) in the γ band. With the help of a tight-binding calculation, we find that the orbital-selective doping effect is due to variation in the spin-orbit coupling (SOC) strength. Our findings not only elucidate the mechanism of LTs in the γ band in SRIO but may also open new avenues for novel SOC-controlled orbital-selective phenomena.