Over 30 planetary systems have been discovered to reside in binary stars. For small separations gravitational perturbation of the secondary star has a strong influence on the planet formation process. It truncates the protoplanetary disk, may shortens its lifetime, and stirs up the embedded planetesimals. Due to its small semi-major axis (18.5 AU) and large eccentricity (e=0.35) the binary $gamma$ Cephei represents a particularly challenging example. In the present study we model the orbital evolution and growth of embedded protoplanetary cores of about 30 earth masses in the putative protoplanetary disk surrounding the primary star in the $gamma$ Cep system. We assume coplanarity of the disk, binary and planet and perform two-dimensional hydrodynamic simulations of embedded cores in a protoplanetary disk. The presence of the eccentric secondary star perturbs the disk periodically and generates strong spiral arms at periapse which propagate toward the disk centre. The disk also becomes slightly eccentric (with e_d = 0.1-0.15), and displays a slow retrograde precession in the inertial frame. For all initial separations (2.5 to 3.5 AU) we find inward migration of the cores. For initial semi-major axes (a_p gsim 2.7), we find a strong increase in the planetary eccentricity despite the presence of inward migration. Only cores which are initially far from the disk outer edge have a bounded orbital eccentricity which converges, roughly to the value of the planet observed in the $gamma$ Cep system. We have shown that under the condition protoplanetary cores can form at around 2.5 AU, it is possible to evolve and grow such a core to form a planet with final outcome similar to that observed.
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