The seismic anisotropy of the Earth's core is believed to be due to a preferred orientation of hexagonal close packed (hcp) iron crystals that constitute the dominating element in the inner core. In this connection, the magnetic properties of the hcp iron in an external magnetic field are very interesting and are studied here by employing an ab initio full-potential linear muffin tin orbital method. By this means the magnetic susceptibility chi of hcp iron and its anisotropy energy for pressures and temperatures corresponding to the Earth's inner core conditions have been evaluated in the framework of the local spin density approximation. The accuracy of this method has been validated by calculating the anisotropic susceptibility of paramagnetic transition metals that form in the hcp crystal structure at ambient conditions. Our calculations demonstrate that for hcp iron the anisotropy of chi is dependent on the c/a ratio. In conjunction with recent data on the c/a ratio and elastic constants of hcp iron, the magnetic anisotropy can explain the seismic anisotropy of the Earth's inner core.