We present results from a three-dimensional particle-in-cell simulation of plasma turbulence, resembling the plasma conditions found at kinetic scales of the solar wind. The spectral properties of the turbulence in the subion range are consistent with theoretical expectations for kinetic Alfvén waves. Furthermore, we calculate the local anisotropy, defined by the relation k_{∥}(k_{⊥}), where k_{∥} is a characteristic wave number along the local mean magnetic field at perpendicular scale l_{⊥}∼1/k_{⊥}. The subion range anisotropy is scale dependent with k_{∥}<k_{⊥} and the ratio of linear to nonlinear time scales is of order unity, suggesting that the kinetic cascade is close to a state of critical balance. Our results compare favorably against a number of in situ solar wind observations and demonstrate-from first principles-the feasibility of plasma turbulence models based on a critically balanced cascade of kinetic Alfvén waves.