In collinear altermagnets, the real-space rotational symmetry of opposite spin sublattices generates a large nonrelativistic spin-splitter current. Orbital transport in this setting has remained largely unexplored. Here, we introduce the orbital-splitter current (OSC), an orbital analogue of the spin-splitter current, and derive its Drude and orbital Berry curvature contributions using a density-matrix framework. We show that the d-wave altermagnet FeSb2 realizes a purely intrinsic OSC because mirror symmetries suppress the Drude channel by forcing the orbital magnetic moment to vanish. The OSC response is strongly anisotropic and for selected field orientations it can significantly exceed the spin-splitter current. Furthermore, using an effective altermagnet-ferromagnet model, we show that the OSC can generate a field-like torque and the combined action of the orbital- and spin-splitter currents can reduce the magnetization switching time.