  We propose a new relativistic Lorentz-invariant spin-noncommutative algebra.
Using the Weyl ordering of noncommutative position operators, we build an
analogue of the Moyal-Groenewald product for the proposed algebra. The Lagrange
function of an electromagnetic field in the space with spin noncommutativity is
constructed. In such a space electromagnetic field becomes non-abelian. A gauge
transformation law of this field is also obtained. Exact nonlinear field
equations of noncommutative electromagnetic field are derived from the least
action principle. Within the perturbative approach we consider field of a point
charge in a constant magnetic field and interaction of two plane waves. An
exact solution of a plane wave propagation in a constant magnetic and electric
fields is found.
