We have studied the phase diagram of MgB\(_2\) superconductor using a single crystal for \({\bf H}\parallel c\)-axis. For the first time we report the existence of peak effect in the screening current in MgB\(_{2}\) single crystal for \({\bf H}\parallel c\)-axis. In the magnetic field regime \(10<H<13.5\) kOe the local fundamental diamagnetic moment displays a very narrow diamagnetic step, with a temperature width of the same size as the zero dc-magnetic field transition. For higher field this step is transformed to a peak which is related with the peak effect in the screening current. Finally, for \(H<10\) kOe the diamagnetic step is transformed to a gradual transition. Our findings for the vortex matter phase diagram for the MgB\(_2\) are closely related with theoretical predictions concerning the vortex matter phase diagram of a type II superconductor in the presence of weak point disorder.