By means of first-principles calculations we predict that it is possible to manipulate the magnetization and magnetization direction in narrow zigzag silicon carbon nanoribbons (ZSiC NRs) by carrier (hole and electron) doping. Without doping, the ground state of the ZSiC NRs wider than 0.6 nm is ferrimagnetic with local magnetic moments at the edge atoms C and Si that are passivated by the hydrogen atoms, and their orientations are parallel at each zigzag edge and are antiparallel between the two edges. Consequently, the magnetic moment per cell of the ZSiC NR is almost zero. It is found that the hole doping enhances the local magnetic moment at the edge C atoms, but weakens the local magnetic moment at the edge Si atoms. As a result, the ZSiC NR is magnetized, and the magnetization direction conforms to the local magnetic moment at the edge C atoms. In contrast, the electron doping weakens the local magnetic moment at the edge C atoms, while it enhances the local magnetic moment at the edge Si atoms. As a result, the ZSiC NR is also magnetized, and the magnetization direction conforms to the local magnetic moment at the edge Si atoms. Thus, the magnetization direction of the ZSiC NRs depends on the type of carrier doping.