We report on the results of x-ray absorption (XAS), x-ray magnetic circular dichroism (XMCD), and photoemission experiments on {it n}-type Zn$_{1-x}$Co$_x$O ($x=0.05$) thin film, which shows ferromagnetism at room temperature. The XMCD spectra show a multiplet structure, characteristic of the Co$^{2+}$ ion tetrahedrally coordinated by oxygen, suggesting that the ferromagnetism comes from Co ions substituting the Zn site in ZnO. The magnetic field and temperature dependences of the XMCD spectra imply that the non-ferromagnetic Co ions are strongly coupled antiferromagnetically with each other.