Stream instabilities arising from anisotropic electron velocity distribution function (EVDF) are discussed in the optical-field ionization mechanism of a monatomic dilute gas by a circularly polarized laser beam in a fully relativistic regime. It is shown that a relativistically rotating electron beam is derived by a circularly polarized laser field with (p_z>p_perp). We show that the following ionization and before collisions thermalize the electrons, the plasma undergoes Buneman and Weibel instabilities. The Weibel and Buneman modes are co-propagating with k normal to the streaming direction. The theoretical results reveal that for the threshold of the relativistic regime (a_0approx 1), instabilities are aperiodic and grow independently. However, by increasing the laser intensity for a_0>1, two instabilities are coupled. The coupling process increased the growth rate of Weibel instability, while the Buneman instability experienced a decrement in its growth rate. For more intense laser radiation, both instabilities are broken into different oscillatory and aperiodic modes.