  We carry out \textit{ab initio} study of ground state phase diagram of
spin-1/2 cold fermionic atoms within two-fold degenerate $p$-band of an
anisotropic optical lattice. Using the Gutzwiller variational approach, we show
that a robust ferromagnetic phase exists for a vast range of band fillings and
interacting strengths. The ground state crosses over from spin density wave
state to spin-1 Neel state at half filling. Additional harmonic trap will
induce spatial separation of varies phases. We also discuss several relevant
observable consequences and detection methods. Experimental test of the results
reported here may shed some light on the long-standing issue of itinerant
ferromagnetism.
