The inverse Faraday effect induced in magnetic films by ultrashort laser pulses allows excitation and control of spins at gigahertz and sub-terahertz frequencies. The frequency of the optically excited magnetization precession is easily tunable by the external magnetic field. On the other hand, the initial phase of the precession marginally depends on the magnetic field. Here we demonstrate an approach for the control of the precession phase by variation of the pump beam direction. In particular, we consider the case when the magnetization precession is excited by obliquely incident pump pulses in a magnetic dielectric film placed in the in-plane magnetic field. Theoretical consideration predicts that the initial phase should appear for a non-zero in-plane component of the pump wavevector orthogonal to the external magnetic field. Experimental studies confirm this conclusion and reveal that the phase grows with increase of the in-plane wavevector component. Variation of phase by 15 deg is demonstrated. Potentially, the phase could be changed even more pronouncedly by more than 90 deg. This work provides a simple way for additional manipulation with optically excited magnetization dynamics, which is of importance for different spintronic applications.