We discuss the problem of universe acceleration driven by global rotation. The redshift-magnitude relation is calculated and discussed in the context of SN Ia observation data. It is shown that the dynamics of considered problem is equivalent to the Friedmann model with additional non-interacting fluid with negative pressure. We demonstrate that the universe acceleration increase is due to the presence of global rotation effects, although the cosmological constant is still required to explain the SN Ia data. We discuss some observational constraints coming from SN Ia imposed on the behaviour of the homogeneous Newtonian universe in which matter rotates relative local gyroscopes. In the Newtonian theory Ωr,0 can be identified with Ωω,0 (only dust fluid is admissible) and rotation can exist with Ωr,0 =Ωω,0 ≤ 0. However, the best-fit flat model is the model without rotation, i.e., Ωω,0 =0. In the considered case we obtain the limit for Ωω,0>-0.033 on the confidence level 68.3. We are also beyond the model and postulate the existence of additional matter which scales like radiation matter and then analyse how that model fits the SN Ia data. In this case the limits on rotation coming from BBN and CMB anisotropies are also obtained. If we assume that the current estimates are Ωm,0 ~ 0.3, Ωr,0 ~ 10-4, then the SN Ia data show that Ωω,0 ≥ -0.01 (or ω0 > 2.6 · 10-19 rad/s). The statistical analysis gives us that the interval for any matter scaling like radiation is Ωr,0 ∈ ( - 0.01, 0.04).